VSWR stands for Voltage Standing Wave Ratio and is a measure of the how well matched a transmission line (e.g. your antenna cable connected to the VHF output of your WatchMate) is to its termination impedance (e.g. your antenna). VSWR can be thought of as a comparative measure of how much power, generated from your WatchMate or XB Transponder, is delivered to the antenna and how much of it is reflected back and lost in the poorly matched transmission line. You care about this as it will effect your transmission performance. A high VSWR will reduce your effective transmission range and can also lead to other problems. If your WatchMate is reporting a problem with your antenna connection or high VSWR, please look at the previous FAQ for troubleshooting.
To learn more about VSWR there is a great explanation given at Microwaves101.com. For those not technically inclined all you have to concern yourself with is ensuring that the cables and connections from your WatchMate to your antenna are sound and your antenna is well matched at AIS frequencies (162MHz) and is not mounted too close to any large metal objects.