Inspired triggers whenever a creature with the ability becomes untapped. Most commonly you'll see it written as "Whenever ~ becomes untapped, [effect]." You tap the creature (usually by attacking), then untap it later—often during your next untap step—to trigger the ability and reap the benefit.
The big nuance: Inspired only triggers on untapping, not on attacking or being tapped. So a creature that's already untapped won't trigger it; it must go from tapped to untapped. Effects that untap your creatures mid-turn (like vigilance-granting tricks won't help, but actual untap effects) can trigger Inspired repeatedly within a turn, which is the key combo angle.
In Commander, Inspired creatures pair well with cards that tap then untap them on demand—untappers, Seedborn Muse, or repeatable untap outlets—letting you fire the ability every turn or even multiple times for snowballing value.