The direction of positive is a matter of choice. Pick a direction to call positive. Anything going the other way will therefore have a negative velocity. A negative acceleration means a velocity getting more negative (either a positive velocity slowing down, or a negative velocity speeding up).
As an example, when we throw a ball up in the air, we define "up" as positive. Gravity, pulling down, is negative. The velocity is initially positive as the ball rises, but when it starts falling again the velocity is negative.
