A "Lead Out" is a sprinting technique often used by the lead-out rider where the rider will accelerate to maximum speed close to the sprint point with a teammate in tow.
The sprinter is normally drafting behind the lead-out rider, hoping to create space between the sprinter and the rest of the pack, saving energy for the attack.
When the lead-out rider in front is exhausted, he will move to the side to allow his teammate to take his place and race for the sprint finish. Often a line of lead out cyclists will be used to form a lead out train to drive the speed higher and higher (and to reduce the chances of other riders attacking) over the closing stages of a race.
The purpose of a lead out is for the sprinter to achieve high speed at the sprint approach using as little of his own energy as possible, so he has as much energy as possible for the final sprint.
Here's a great video by our friends at GCN describing this in great detail:
And another, more-technical video describing the underlying benefits of a draft and lead-out attack: