The team that most improved itself this offseason is… well, hang on a second. We have to explain what "improved" even means, first. The way you'd generally think to do it is to look at team win totals from 2017, compare them to projected win totals from '18 (we'll be using FanGraphs for this), and see what's changed. If you look at it that way, you'd see that the Giants are projected to be 18 wins better. The D-backs appear to be 12 wins worse.
That's the simple way, but it's also not the best way. San Francisco may have lost 98 games last year, but only because everything that could have possibly gone wrong did go wrong. Madison Bumgarner, Johnny Cueto, Will Smith, Hunter Pence, Brandon Belt and Mark Melancon all got injured; Brandon Crawford had an unexpected off year; and a dozen other things all went the wrong way. It's hard to imagine that all happening again.
Ninety-eight losses is 98 losses, to be sure, but the Giants didn't bring a 98-loss roster into the offseason. (No one would suggest San Francisco had a lesser roster than, say, the 95-loss White Sox, for example.) Since the true talent level was higher than that, if they'd done absolutely nothing at all, they'd still be expected to improve in 2018.
The Giants did a whole lot more than "nothing" this offseason, of course, as we'll get to in a minute. The point here is that we want to find a way to separate a likely improvement between "the talent already on the roster" and "pieces added this offseason." The way we do that isn't to look at 2017 record; it's to look at what the '18 projections said at the end of the season, before any moves were made.
We can do that by comparing the 2018 projections of Nov. 12 to the ones we see today. (Why Nov. 12? To be honest, it's because that was the closest to the end of the 2017 season we could pull up on the Internet Archive, but it works well enough for our purposes here, because other than player options being exercised, no major moves happened until the Mariners tradedEmilio Pagan for Ryon Healy on the evening of Nov. 15.)
By that view, the Giants weren't a 64-98 team coming into the offseason, they were a 78-84 roster. They're better than that now, obviously, having made some moves this offseason. But they're not the most improved team. It's the Yankees. Of course.

Yankees (+6)
After winning 91 games last year, the Yankees were projected for 89 on Nov. 12. That's already pretty good; it's difficult to improve much on that. Of course, then they went out and added Giancarlo Stanton, Brandon Drury and Neil Walker to an already-strong roster that's expecting more contribution from Greg Bird, Gleyber Torres and Miguel Andujar this year, while also further reducing opportunity for the unproven Clint Frazier and the disappointing Jacoby Ellsbury. Now, the projection is 95 wins. Hard to argue with that. No team added more projected value than the Yanks.
Brewers (+5)
Right behind the Yankees are the Brewers, and doing it this way is a much better look, because while Milwaukee won 86 games last year, it entered the offseason projected for just 73 wins, in part because ace Jimmy Nelson is injured and will miss a chunk of the season. It's better now, at 78 wins, since the Brewers later added outfielders Lorenzo Cain and Christian Yelich, and while that still feels low, that's largely because the only additions to a thin rotation were journeymen Wade Miley and Jhoulys Chacin. At least this way, they're +5, not -8. They've clearly gotten better. 

Giants (+4)
Blue Jays (+4)
Padres (+4)
Rounding out the top five are three teams who added four projected wins: the Giants, Blue Jays and Padres 
That's most notable in San Francisco, as the Giants added Evan Longoria, Andrew McCutchen, Austin Jackson and Tony Watson, who should each help. It's not just about who arrived, however; it's also about who lost playing time as a result of the moves. Player Page for Matt Cain retired, while Denard Span and Matt Moore were traded; in addition, Pablo Sandoval now has less of a path to playing time. The Giants will be several wins better simply due to expected better health; these gains are on top of that.
The Jays have the same health hopes as the Giants -- full seasons from Josh Donaldson, Devon Travis and Aaron Sanchez would be nice, though Troy Tulowitzki is still ailing -- but we're simply talking about external additions here. Randal Grichuk, Curtis Granderson, Yangervis Solarte, Aledmys Diaz and Seunghwan Oh may not be All-Stars, but they're filling in some enormous gaps, particularly in the corner outfield. (Toronto had the American League's weakest outfield last year.)
Finally, San Diego isn't likely to contend this year, but it certainly got better, having added veterans Eric Hosmer, Freddy Galvis, Bryan Mitchell and Chase Headley. 
Phillies (+3)
Rangers (+3)
Red Sox (+3)
White Sox (+3)
Astros (+3)
Within this final group, you have the 2017 World Series champions, the two-time defending AL East winners, and the complete rebuild on the South Side of Chicago. There's many ways and places to add wins.

For the Astros (Gerrit Cole) and Rangers (Mike Minor, Doug Fister, Chris Martin, Moore), it was largely about adding pitching, though the two staffs started from different places. The Red Sox did very little this offseason, yet their extra three wins can be explained almost entirely by the addition of J.D. Martinez, the best bat of the offseason. And the Phillies, of course, added Jacob Arrieta, Carlos Santana, Pat Neshek and Tommy Hunter.
As for the White Sox, it's true that a win or two or three here or there won't make that much difference as they rebuild. That said, they did add Welington Castillo and Joakim Soria, both solid Major Leaguers. The projections have them as improved, though surely the main priority this year is that Yoan Moncada, Michael Kopech, Lucas Giolito and friends continue to advance.
The rest
"Where," you might be asking, "is [my favorite team]? The Rockies, Angels and Twins made so many moves." Well, the first thing to remember is that projections are estimates; they're good, but they're not perfect or infallible. Sometimes they're even wrong. They might be wrong! We can at least explain why they see things that way, however, for those three teams.
For the Rockies, it wasn't about lack of moves, so much as it was the net effect of those moves. Their big splash was in the bullpen, where they retained Jake McGee and added Wade Davis and Bryan Shaw. That's going to be a good group; however, they were already a good group, ranking sixth in the most advanced Statcast™quality of contact metric. Davis and Shaw essentially replace Greg Holland and Neshek, and since Colorado brought back both McGee and Carlos Gonzalez from last year's team, the actual improvement is muted.

It's different for the Angels and Twins, partially because wins don't come in a vacuum. If you add wins, someone else has to lose them. (That is, there's only so many games in a season; you can't have everyone projected for 90 wins, for example.) So any projected win added by one club has to result in a projected win lost from another club. It has to even out.
So yes, the Angels got better, having added Ian Kinsler, Shohei Ohtani and Zack Cozart, though they gave back a little of it when they traded C.J. Cron and entrusted more first base time to Jose Pujols. The problem is that the rest of their division got better too, from the Rangers remaking their pitching staff to the already-dominant Astros adding Cole and Joe Smith to the A's adding three good relievers along with Jonathan Lucroy.
For the Twins, while they've added Lance Lynn and Jake Odorizzi, neither moves the needle that much, and they've given back some of that rotation boost with the news that Ervin Santana could be out for at least the first month (if not more) due to finger surgery, as well as continued questions about Miguel Sano's availability as he recovers from surgery and awaits a ruling on a sexual assault accusation. Logan Morrison, however, was a nice under-the-radar addition. 
All that said, projections aren't perfect and aren't intended to be, though for what it's worth, a separate system at Baseball Prospectus also views the Rockies, Angels and Twins in the same 78- to 83-win range.
When the 2018 season plays out, a team like the Giants is going to have had the largest increase in wins, simply because they massively underperformed their expectations last year. They were always better than that, though, and it's a lot easier to add wins to a 64-win season than it is to add to a 91-win season, which the Yankees are coming off. Despite that, the Yanks have still "won the offseason," at least by this view. It's merely the first of what looks to be many, many Yankees wins in 2018.