If the derivative is positive on an interval, the original function is increasing on that interval. If the derivative is negative on an interval, the original function is decreasing on that interval.
Concavity describes the direction a function is bending. A function is concave up on an interval, then the second derivative is positive on that interval and the function bends upwards. A function is concave down on an interval, the second derivative is negative on that interval and the function bends downwards.