Low latency is exactly what you want. The lower your latency, the quicker the response is between you and the server. A high latency is bad, and is what online games will wanr you about.
While even the oldest of routers should process any home connection just fine, under normal conditions, if his actual connection is under high load due to torrenting, downloading, uploading, or the router itself is bad, it can cause higher latency than normal.