In The Walking Dead: March to War Talents are options that give a Survivor or a Council Member a specific enhancement or 'buff' to certain stats (usually their Traits). Some Talents are more specific and only take effect in particular situations such as on Missions, when Scavenging, or when Attacking. And some of them affect not the Survivor but the Council Member that's leading their Raid Party.
Every Survivor has Talents, some will already have them when they are recruited while others you will have to wait until the Survivor reaches a certain level before they recieve them. As you build your team you will see members of all classes with talents from every class. Some Survivors will have Talents that specialise in combat which makes them ideal for Walker Missions while others may have Talents that are more suitable for gathering supplies in Supply Misssions. Mastery of the Talent system is important as it allows you to devise unique strategies, effective defenses and devastating attacks which can mean the difference between going through the game living comfortably or struggling to just stay alive if you get the balance wrong.
Whenever you see a Talent badge the colour will indicate its rarity (and relative value) of the Talents offered:
Gray or White Talents are Common.
Green Talents are Uncommon.
Blue Talents are Rare
Purple Talents are Epic
Gold Talents are Legendary