What does -9.8 m/s mean? and what does it mean if something has a negative velocity?

I can't guess what -9.8 m/s means until you tell me where it came from,
or what 'm/s' means.

If perhaps it has something to do with the acceleration of gravity on Earth,
then the correct figure is ' -9.8 m/s² '.  That means that any object that
has no other force acting on it except gravity has its speed changing by
9.8 meters per second every second.  Since it's gravity doing the job,
then the object's speed is either increasing down, or decreasing up. 

If an object has negative velocity, then it's moving in the direction opposite
to the direction that you decided to call positive when you started doing the
problem.

For example, if you decide that up is positive and down is negative, and
then somebody drops a stone from the top of a tall building, then the
gravitational force on the stone is negative (pointing down), its velocity
is negative (it's falling towards down), and its acceleration is negative (its
speed towards down is getting faster and faster).  Everything is negative,
only because you decided that up is positive and down is negative.  It's
nothing to be worried about.

Rain is pulled by gravity which is a non contact force