This move is a weak opening because it develops the queen too early and subjects it to attack, and deprives the knight of its best square.
As with the similar 2. Qh5, White hopes for the scholar's mate: 2.Qf3 Nc6 3.Bc4 Bc5?? 4.Qxf7#. In both cases, Black can easily avoid the trap. However, the Parham Attack is more forcing and stronger—first requiring Black to defend his e-pawn (usually with 2...Nc6), then after 3.Bc4 forcing Black to play a sub-optimal move (3...g6 virtually committing Black to a fianchetto rather than a more aggressive placement of the bishop; 3...Qe7 blocking the bishop; or 3...Qf6 taking away the knight's best square). 2.Qf3 places no such impediments on Black's development.