Here is what Martino has already brought us.
1. Restoration of the pressing game. This has resulted in us being much more solid in defense.
2. Rotation of squad. Allows us to play a pressing game without key players getting tired, and allows younger players a chance to break into the team.
3. Vertical play. People are saying that Martino brings us counter attacking football, that's not strictly what has happened. What has happened is that when we have possession, more players, including midfielders, are encouraged to make runs forward. So instead of having 4 options all within 15 yards and in deep "safe" positions, we now have times where a player will break forward, to either receive the ball and advance the team, or drag a defender with him. This is especially true with the wide players, with us playing lots of diagonal long passes, and that creating plenty of new chances for us.
The biggest point is our last point. The reason I think we got beaten so badly last year, was that our players had no options to move the ball forwards, no players were making runs into advanced positions. This resulted in two problems. Firstly, we had no way to create a goal scoring chance, and often resorted to long shots. Secondly, it meant that teams like AC Milan and Bayern especially could press us extremely aggressively, extremely high up the pitch, with quite literally no risk of barca pinging a long pass forward to relieve the pressing and create a goal scoring chance. We couldn't threaten them. I also think it is why we struggled to score goals against some of the top teams last year, especially when we didn't have Messi. Only when we had Messi, did we have the incisiveness to move the ball forward.
Edit:
The whole possession thing that many Barcelona fans are whining about is silly. Against Rayo, they were the team that had the second highest possession in la liga last season, they also had the vast majority of their "possession," along the back four. Tata's tactics were spot on for that game, he pressed when they put the ball into midfield, and once we had a lead there was no need to chase the game when they were passing it along the back four.