Suspend lets you cast a card from your hand for an alternate cost by exiling it with a number of time counters on it. At the start of each of your upkeeps, you remove one time counter; when the last one comes off, you cast the spell for free (no mana cost). If it's a creature, it also gains haste until you lose control of it.
The big rule people miss: when suspend resolves, you cast the spell—it still goes on the stack and can be countered, and it must have legal targets. It's not a free entry onto the battlefield. Also, you must cast it; you don't have a choice once the last counter is removed.
In Commander, suspend matters for telegraphing big threats early and dodging mana costs, but the delay gives opponents a full turn cycle to prepare counterplay or removal.