Acceleration gets you up to speed faster. This means you will get some not inconsiderable seperation depending on the aircraft involved , even if you have a lower top speed.
You can build up speed faster, and use that speed to initiate a zoom climb which your opponent (being at a lower speed) likely can't follow (again, depending on the aircraft).
Acceleration could theoretically help you in a dive, although your diving ability is determined more by your aircraft's stuctural limits and high-speed handling than by dive speed and acceleration in a dive. The 109K, for example, accelerates like a banshee, even in a dive compared to other aircraft. IIRC, only the 190D and La-7 are clearly ahead of it out of all non-perked aircraft in level acceleration, to give you an idea of the power it has. However, it would be described as an average diver at best, leaning more towards the "poor" end of the spectrum, due to its handling characteristics, and low compression speed.
If you have better acceleration, you'll be better in a sustained turn fight than another aircraft with an equal wing loading, but worse acceleration. This is because you'll slow down less in the turns, and you'll drop to your minimum speed slower than the other aircraft.
Its also invaluable in an energy fight. Say a Typhoon is BnZing a 109K from a 2k alt advantage. Realistically, the Typhoon will only have a few passes before the 109K equalizes the energy states, and starts to take the advatnage. The K4 peaks at over 4500ft/min climb rate at low altitude, and it only takes slightly over 2 mintues to make 10,000ft, and effortlessly out accelerates the Typhy. The Tyhpoon also retains energy rather poorly, only compounding the problem.
Acceleration is almost always accompanied by a good climb rate, IIRC, so you can usually count on that to help you build energy along with your pure level acceleration.
