Swingby

Swingby is the colloquial term for 'gravitational/gravity assist manoeuvre' or 'sling-shot'. The basic principle is to use the relative motion of a massive body (a planet usually) to steal some momentum in order to accelerate or decelerate a spacecraft. This sounds like cheating, but it really works. The velocity relative to the Sun can be changed, but the speed relative to the swingby planet stays the same. Optimising swingby plans is a fun challenge in astrodynamics. 

You can read up on Gravity Assists in wikipedia, or elsewhere, including many excellent books.

As a real example of a swingby, check out this page for a good description and some vector diagrams of the Nozomi Earth Swingby manoeuvre. However the really classic example of this comes from the Voyager 2 Grand Tour:

Spacecraft speed with spikes at each planet caused by swingby
(note how the Jupiter swingby gave Voyager2 enough speed to escape the gravity of the Sun!)