Their shot quality has improved quite a bit since about the beginning of March.
From the start of the season to the end of February, pbpstats has the Celtics shot quality (expected effective field goal percentage based on a variety of factors) as 50%, 28th of 30 teams. Their TS% over that span was 56.46, 20th in the league.
Since March 1st, the Celtics shot quality is 52% (15th and roughly league average) with a TS% of 59.47, 4th in the league.
Other relevant stats:
Rim or 3 Frequency: Start-Feb28: 63.7% (23rd) Since March1: 70.84% (14th)
FG% at the rim: Start-Feb28: 65.87% (10th) Since March1: 69.67% (2nd)
March 1st isn't some magic date, of course. The point is that they've been much better on offense the past couple months.
The reason? JT and JB are taking fewer bad shots and have been better at finishing at the rim (well, looking at the stats, it's all Tatum here). That's been the primary difference to my eyes.
Edit: To finish up on this:
Rim or 3 frequency Start->Feb28: JT: 55.52%, JB: 57.36%
Rim or 3 frequency Since March1: JT: 65.44%, JB: 69.33%
Rim fg% Start->Feb 28: JT: 61.72%, JB: 71.05%
Rim fg% Since March1: JT: 76.15%, JB: 64.71%