A 'reception' in football is when the ball is caught by an eligible receiver after a forward pass. It is another word for a catch. However, there are some distinctions on what is considered a reception.
Eligible receivers include the running back, tight end, and wide receivers. A reception can have a positive or negative connotation as in the reception can be for a gain of yards as well as a loss of yards. A reception is officially declared after the ball is caught and the receiver makes a 'football move', or a move that declares possession of the football. Football moves include bringing the ball to the chest, taking multiple steps, or performing a ball carrier move (such as a juke or spin). After possession is made, a reception is recorded. The ball carrier can fumble the football after the reception, but if they hadn't made a football move, it is declared an incomplete pass.
It's important to note that a reception is different than a lateral pass. Also called a backward pass, any sideways or backward pass isn't considered a reception. A reception only moves the ball forward, not toward the opponent's end zone.