If the object undergoes a change in velocity from +1 m/s to +4 m/s, its velocity is becoming more positive. This means that the magnitude of the velocity vector increased (from 1 to 4) while the direction of the vector remains the same as the positive direction of a coordinate axis.
If the magnitude of the velocity vector had decreased while its direction remained the same as the positive direction of the coordinate axis, then velocity would have become less positive.
The acceleration is positive because it is equals to the change of the velocity in a unit of time:
Since the change in velocity is positive: 4 - 1 = 3, the acceleration is positive.