A dazzling sleight of hand trick is card vanishing and production. A simple trick like the "rub vanish" involves putting the card on the table under one hand and watching it "vanish." In reality, you simply slide the card back onto the deck without detection by the spectator.
Using the absolute system of math, you can create the illusion of magic just from properly dealing the deck. In the "It's your deal" trick, you begin with an evenly cut deck that is sorted into four piles. One of those four get dealt again into four piles. With the uneven pile discarded you can mathematically pick the middle card out of the middle pile as the chosen card.
A mental card trick is a where you incorporate the spectator's involvement with the trick itself. Coaxing his card selection combined with sleight of hand creates the illusion. It can be as simple as remembering the bottom card of a deck and then through a series of shuffles and pile separation convince the spectator he chose the card you pre-selected.