2 pieces give you a bonus chance for hull repair which will give you up to 30% of your hull back.
3 pieces gives you a chance for a shield heal bonus which happens when your shields go below 20%.
4 pieces gives you a lame tractor beam.
Up until now, everyone has been using the borg engines, deflector, assimilated module (for the hull and shield healing set bonuses) and the MACO shield (which is the best shield in the game).
After season 7, they're removing the assimilated module as a set piece and making it a part of its own set. So, to get the 3rd set bonus shield heal I described above, you have to use the lame Borg shield.