To activate a Spell/Trap Card is to play it on the field face-up, either from your hand or flipping it face-up after it was Set, and usually you declare that you want to apply its effect if it has any. Trap Cards and Quick-Play Spell Cards cannot be activated during the same turn they were Set.
To activate an effect is to declare that you want to apply it. This goes for Flip, Trigger, Ignition and Quick Effect of Effect Monsters and also for Trigger-like, Ignition-like or Quick-like Effect of Spell/Trap Cards. Effects can be activated not just when the card is face-up on the field, but also in the hand, Graveyard, Banished Zone, Main and Extra Deck, depending on what the card says.
Note that "activating a card" is different from "activating the effect of a card." For example, some effects - like "Magic Jammer" and "Skilled Dark Magician" - only apply when a Spell Card is activated, but do not apply when the "effect" of a Spell Card is activated.
Any activated card or effect must have a Spell Speed. You cannot activate a card effect which has lower Spell Speed than the effect on the Chain Link before it. Effects which do not have Spell Speeds are never activated; and never start any Chain Link.
You cannot activate a card effect that its condition didn't meet, knowing that it cannot resolve properly. For example, you cannot activate "Lightning Vortex" knowing that your opponent controls no face-up monsters to destroy.
You cannot activate a card effect in the middle of the resolution of another activated card effect, or during an action that did not finish yet. Only cards like "Bait Doll" can make that permissible to its targets.