All combatants make an initiative roll at the start of combat. This roll determines the order in which characters act. A higher initiative may be important to certain classes that benefit from acting early in a fight. This includes rogues with first strike, defenders, and so on; however, nearly all characters will prefer to act early rather than late.
The primary attribute for initiative is Dexterity, though other stats may be used through the use of feats (for example, Wary Fighter). Other effects can add modifiers, such as bonuses from feats and class features or penalties from circumstance or monster powers.
Initiative = d20 + Dexterity Modifier + Initiative Modifiers
The character with a higher initiative roll acts first in combat, followed by the next-highest and so on. Typically player characters roll their own initiative (though the DM may handle this as well), and the DM handles rolling the initiatives of NPCs (both friendly allies and monsters), traps, and other entities that will take turns in combat.
Example feats that affect Initiative rolls (not a complete list):
Initiative in gaming culture
The use of initiative to determine combat order dates back to the first edition of Advanced Dungeons & Dragons in 1977. A Dungeon Master's instruction to the players to roll initiative has become an iconic signal that a combat encounter has begun. By extension, in broader gaming culture, a threat or a demand to roll initiative humorously signifies an ambush, imminent combat, or a challenge to combat.