Space travel with constant acceleration means accelerating at a steady speed in order to get to another place quickly. Constant acceleration means the speed you're going will keep getting faster and faster, like a car accelerating on a flat road. But instead of the car going faster on the ground, the space craft will be going faster in space.
This works because the bigger the speed you have, the bigger the distance you can travel. When a space vehicle accelerates at a constant speed, its speed keeps getting bigger, like a rollercoaster car going up a hill. The higher the speed, the farther it can travel in a shorter amount of time. This means it can reach places farther away faster.