A car speeding up
An object moving in a circle
Acceleration is a change in velocity, and as velocity is a vector, it has a magnitude (size) and direction. Therefore, whenever an object is changing direction, it is accelerating. This means, that as a car god round a roundabout, it is constantly changing direction and therefore constantly accelerating.
By the same logic, the earth is actually constantly accelerating around the sun as it orbits.
When a car starts moving and speeds up from still to, say 30 mph, it is accelerating.
Equally, anything that gets faster is accelerating - increasing its speed over time - equally, anything that gets slower - decreasing its speed over time - is deaccelerating.
I hope this helps; let me know if I can do anything else:)