What you will notice is that you can accelerate faster with lighter wheels. Stomp on the pedals and the bike will feel like it responds better.

There's a lot of discussion about whether you will feel this on a climb, with the argument that climbing is about acceleration/deceleration, so you a really always accelerating on your downstroke and decelerating due to gravity at the dead spot in your stroke. I can say that I feel better climbing on light wheels, and I have some evidence that I do go faster (based on my cyclometer readings) but I wouldn't put more than placebo effect faith in them.

The best way to get faster is to ride more and ride faster.