Concentration check in 5e is related to spells with the 'concentration' description. Spells requiring Concentration have a couple unique differences to other spells.
1. You can only have one spell requiring Concentration active at a time. So no more having your Wizard or Cleric cast 76 buffs and become better than your fighter at fighting.
2. If you take damage you have to make a Concentration check (which is modified by your Constitution modifier). If Larian has implemented it like it works in 5e PnP the Concentration DC is 10 or 1/2 the damage taken (whichever is higher). If you take damage from multiple sources you make a separate Constitution Saving throw to maintain concentration for each source of damage taken.
I haven't played the early release, but just figured I'd at least provide you with the detail on how concentration works based on 5e rules.
