You can find a good article here: http://en.wikipedia.org/wiki/Terminal_velocity
In the context you provide, terminal velocity is the maximum speed that an object in free fall reaches in the atmosphere.
When an object is falling, or in free fall, there are two forces that determine whether it will accelerate downwards or not:
- gravity (trying to accelerate the body downwards)
- air friction (trying to push the body upwards)
Initially, as the body is not moving, there is no air drag, and the object starts falling due to gravity.
Now, as the object speeds up, the gravity contribution remains constant, whereas the drag increases with the speed of the object.
Finally a point is reached where the drag is so much that the object does not accelerate anymore. Velocity stays constant and it is called terminal velocity.
The value for it is proportional to $\sqrt{m}$ so clearly objects of different weights have, in general different terminal velocities (heavier objects having higher values), but there are also other factors to account for, like how aerodynamic the object is. A sphere has higher terminal velocity than a sheet of metal of the same mass.