Talents provide a unique combat enhancement triggered through defined activities in The Division. While 4 Talents can be equipped simultaneously, every Talent “affects” something. The Precision Talent for example affects the enemy when activated, but others could probably affect your own character, allies, or other combinations of this.
The unlocking process is directly tied to your mission progress and once you have unlocked them, you can freely swap between them. A list of all available Talents can be found in the Skill Calculator.