Jace, Telepath Unbound's second ability states that "If the card (the spell cast from the graveyard) would be put into the graveyard this turn, exile it instead." This means whatever spell you pull from the graveyard, if it were to return to the graveyard by any means (casting, countered, etc,.) then the card gets exiled instead of going to the graveyard. In short, when you use Jace's second ability, any card you cast from the graveyard will most likely be exiled.
There are ways to prevent this with other spells or abilities. For example, if you cast a spell with Buyback (e.g., Walk the Aeons), it never goes to the graveyard, and Jace's ability will not exile it. Likewise, if you cast a spell from your graveyard and then Remand your own spell, it returns to your hand.