Alpha Strike is a term referring to the initial attack by enemy spawns or singular critter, such as an Archvillain. Due to how the game mechanics work, the first person the enemy sees is the single target the entire spawn will focus their ranged attacks on, which can often mean defeat in larger teams for players who have lower hit points than that of other Archetypes, such as a Blaster or Dominator.
With this in mind, Taking the Alpha means one of the team will go in and take the initial attack from the mob. Once the initial alpha strike has been fired off, the rest of the team join the fight and the enemy's aggro is now divided among the team according to threat levels and taunt effects. Generally a player with defensive or resistant powersets, higher hit points, or able to divert the damage to pets or henchmen is usually the one to take the alpha, though this is not always a rule. Many Blasters, for example, have been known to lead the team into combat by taking the alpha regardless of defences or hit points.
Alpha Strike can also refer to the team action of when all the players direct all their available hard-hitting powers onto one single target at the same time, or as close to it as possible, in effect, doing what the enemy spawns do.