A "negative" is performed during muscular eccentric contraction movement. During this movement, the muscles tighten and elongate. This is opposite of concentric contraction which occurs when the muscles tighten and shorten in length. Most exercises place focus on concentric contraction as means to achieve results.
An example of performing a negative would be to execute a bench press exercise and slowly lower the weight down to the chest before pressing it back to the starting position.
It should be noted that during the prolonged eccentric contraction of the muscles that it is very important to continue breathing and not hold one's breath. This allows for much needed oxygen to continue flowing to the muscles as well as enforce proper weight lifting technique.