Velocity and acceleration are vectors, this means that they have both direction and magnitude.
So when I throw a ball with a certain velocity I should technically also specify the direction; after all I throw it in a certain direction, maybe along the floor or diagonally over the roof of a building; or, as in this question, straight up.
Now, when we are just interested in the magnitude of the velocity and not it's direction it's usually called speed; the same goes for acceleration except there is no usual technical term for this. Generally this is called the magnitude of the vector; and sometimes it's referred to as a scalar meaning that it's a pure number (ie not a vector).
Now, in your question/answer when it says that acceleration is 9.81*m/s*; this is a scalar value and is not specifying the direction.
When it says -9.81*m/s*, this is specifying a direction; to see this we have to specify coordinate axes; since there is no horizontal motion we can neglect that completely, so we just need to specify the vertical axis, this is just a vertical line going through where you are standing and the origin is where your feet touches the ground.
On this axis we just need to specify which is the positive direction and which is the negative direction; the simplest and the standard for throwing questions like this is to specify the upward vertical direction as positive, and hence the downward direction is negative.
Now the force of gravity on the ball acts downward; this gives an acceleration to the ball and this acceleration is also downward; this is why you have a minus in front of the acceleration, ie -9.81*m/s*.