Card effects all have certain speeds. This determines when they can be played and which effect can be "chained" to another.
When a card effect (be it Spell, Trap or Monster) is activated, the other player has the chance to "chain" onto this by activating their own card effects. You can only 'chain' if the 'spell speed' of the card effect you are chaining with is equal to or greater than the effect you are chaining onto. Once no one who is playing wants to chain onto the most recently activated effect, the effects are resolved, in reverse order.
There are 3 Spell Speeds: 1, 2, and 3. You cannot chain spell speed 1 effects to another card effect, and can only activate them during either of your main phases.
The activation of normal spells, continuous spells, equip spells, field spells, and ritual spells are all spell speed 1. Some continuous or field spells can have spell speed 2 effects that can activate during the opponent’s turn or the battle phase.
Quick-play spells, normal traps, and continuous traps are spell speed 2.
Counter traps are the only cards that have spell speed 3 effects, and only other counter traps can be chained to them.
Monster effects can be spell speed 1 or 2, depending on the text. If a monster effect says “During either player’s turn”, or “This is a quick effect”, or has an effect that activates when the opponent declares an attack, at any time during the opponent’s turn, or during the player’s draw phase, standby phase, battle phase, or end phase, it is a spell speed 2 effect. This also applies to continuous and field spells.