An effect in Magic is something that happens in the game as a result of a spell or ability. When a spell, activated ability, or triggered ability resolves, it may create one or more one-shot or continuous effects. Static abilities may create one or more continuous effects.
Staple effects are effects that are put in almost every set by R&D — like counterspells, burn, mana creatures, card draw, and creature removal. 
From the Comprehensive Rules (Amonkhet (April 28, 2017))
- 609. Effects
- 609.1. An effect is something that happens in the game as a result of a spell or ability. When a spell, activated ability, or triggered ability resolves, it may create one or more one-shot or continuous effects. Static abilities may create one or more continuous effects. Text itself is never an effect.
- 609.2. Effects apply only to permanents unless the instruction’s text states otherwise or they clearly can apply only to objects in one or more other zones.
Example: An effect that changes all lands into creatures won’t alter land cards in players’ graveyards. But an effect that says spells cost more to cast will apply only to spells on the stack, since a spell is always on the stack while a player is casting it.
- 609.3. If an effect attempts to do something impossible, it does only as much as possible.
Example: If a player is holding only one card, an effect that reads “Discard two cards” causes him or her to discard only that card. If an effect moves cards out of the library (as opposed to drawing), it moves as many as possible.
- 609.4. Some effects state that a player may do something “as though” some condition were true or a creature can do something “as though” some condition were true. This applies only to the stated effect. For purposes of that effect, treat the game exactly as if the stated condition were true. For all other purposes, treat the game normally.
- 609.4a If two effects state that a player may (or a creature can) do the same thing “as though” different conditions were true, both conditions could apply. If one “as though” effect satisfies the requirements for another “as though” effect, then both effects will apply.
Example: A player controls Vedalken Orrery, an artifact that says “You may cast nonland cards as though they had flash.” That player casts Shaman’s Trance, an instant that says, in part, “You may play cards from other players’ graveyards as though they were in your graveyard.” The player may cast a sorcery with flashback from another player’s graveyard as though it were in that player’s graveyard and as though it had flash.
- 609.5. If an effect could result in a tie, the text of the spell or ability that created the effect will specify what to do in the event of a tie. The Magic game has no default for ties.
- 609.6. Some continuous effects are replacement effects or prevention effects. See rules 614 and 615.
- 609.7. Some effects apply to damage from a source—for example, “The next time a red source of your choice would deal damage to you this turn, prevent that damage.”
- 609.7a If an effect requires a player to choose a source of damage, he or she may choose a permanent; a spell on the stack (including a permanent spell); any object referred to by an object on the stack, by a replacement or prevention effect that’s waiting to apply, or by a delayed triggered ability that’s waiting to trigger (even if that object is no longer in the zone it used to be in); or a face-up object in the command zone. A source doesn’t need to be capable of dealing damage to be a legal choice. The source is chosen when the effect is created. If the player chooses a permanent, the effect will apply to the next damage dealt by that permanent, regardless of whether it’s combat damage or damage dealt as the result of a spell or ability. If the player chooses a permanent spell, the effect will apply to any damage dealt by that spell and any damage dealt by the permanent that spell becomes when it resolves.
- 609.7b Some effects from resolved spells and abilities prevent or replace damage from sources with certain properties, such as a creature or a source of a particular color. When the source would deal damage, the “shield” rechecks the source’s properties. If the properties no longer match, the damage isn’t prevented or replaced. If for any reason the shield prevents no damage or replaces no damage, the shield isn’t used up.
- 609.7c Some effects from static abilities prevent or replace damage from sources with certain properties. For these effects, the prevention or replacement applies to sources that are permanents with that property and to any sources that aren’t on the battlefield that have that property.