Conjure creates a brand-new card out of thin air and puts it into a zone—usually your hand. For example, "conjure a Lightning Bolt into your hand" gives you an actual Lightning Bolt card to cast, complete with its real card text. The conjured card is a genuine card (not a token), so it can be discarded, shuffled into your library, exiled, or otherwise manipulated like any normal card.
The common confusion: Conjure is an Alchemy/Arena-only mechanic. It doesn't exist in paper Magic, so you won't see it in tabletop Commander games. Because it's digital-only, it's not legal in paper EDH at all.
Where it matters: only in Alchemy or Historic Brawl on MTG Arena. There, conjured cards effectively generate card advantage from nowhere, sidestepping your library, which can be powerful for value engines and combo enablers in singleton Brawl formats.