Effect is an indication of the impact that a character's actions have in the game world, i.e. their outcomes and consequences. It is the fourth and final part of the IIEE model of resolution. In mechanical terms, effect is determined after the success or failure (etc.) of a character's actions is known (the execution stage of IIEE), and describes what happens as a result of that execution.
For example, in Dungeons & Dragons 5th edition, a basic attack may hit or miss. Assuming that it hits, the effect is then determined by what happens as a result of the successful attack, which will generally include dealing damage (calculated with a separate damage roll in D&D) or inflicting one or more conditions (depending on the rules of the attack, ability or weapon being used). The damage inflicted can even have other impacts, such as the death of the enemy if damage is higher than the creature's remaining hit points.
It is entirely possible for some games to assume a successful execution but a nil effect, or for the game mechanics to take place entirely at the level of effect. That is, any action is assumed to be executed as described, but the effect of the action is determined using a resolution mechanic (e.g. rolling dice as part of random resolution).