This property indicates if multiple requests can be processed with the same IHttpHandler instance. By default at the end of a request pipeline all http handlers that are placed in the handlerRecycleList of the HttpApplication are set to null. If a handler is reusable it will not be set to null and the instance will be reused in the next request.
The main gain is performance because there will be less objects to garbage-collect.
The most important pain-point for reusable handler is that it must be thread-safe. This is not trivial and requires some effort.
I personally suggest that you leave the default value (not reusable) if you use only managed resources because the Garbage Collector should easily handle them. The performance gain from reusable handlers is usually negligible compared to the risk of introducing hard to find threading bugs.
If you decide to reuse the handler you should avoid maintaining state in class variables because if the handler instance is accessed concurrently multiple requests will write/read the values.