In Magic: the Gathering, summoning sickness prevents creatures from attacking or using activated abilities until their second turn in play. This used to be called summoning sickness, as the idea was the monster you summoned from some arcane shore would need time to acclimate to its new surroundings. The term itself has fallen out of use, but the rule still remains.
Essentially, whenever you summon a creature, it must survive your opponent's next turn before it gets a chance to attack or use any of its activated abilities. It still gets to block, it just can't attack until your next turn. This has two effects on game play:
- The benefit of going first is lessened, since the player that goes first cannot attack before the player going second has a chance to defend.
- Any future attacks with creatures are communicated a turn before the attack comes, giving the defending player a chance to set up a defense.
This mechanic is sometimes called jet lag, dizziness, etc. Ever since seventh edition or so, the name has dropped from the literature but the mechanic has been retained. Other CCGs have stolen — I mean, adapted — this mechanic to their games as well, where applicable.
As with every rule, there is an exception. There have always been creatures with the ability "unaffected by summoning sickness" since alpha. Around fifth or sixth edition this was abbreviated to "haste", much the same way "does not tap to attack" was abbreviated "vigilance". Creatures with haste may attack and use abilities that require tapping the turn they come into play, ambushing the opponent. Red and white creatures are more likely to have haste than any other color. Every card set usually has a red instant which gives haste to a creature for one red mana.
It's been a long time since I've played cardboard crack, so some of these edition numbers may be a bit off.