VSWR - Voltage standing wave ratio (VSWR) in this case is most likely referring tothe/a VSWR meter which measures the standing wave ratio in a transmission line. This is a item of radio equipment used to check the goodness of the match between the antenna and the transmitter. My Uniden BC780XLT has a built in VSWR meter (I think...Dave: feel free to correct me) which shows up as signal strength. Only if your *really* desperate to get a little better signal than you already are with the J-pole, you can tweak this until you become frustrated. I adjusted mine very quickly and didn't find a major difference between different locations.
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VSWR is essentially a measure of the ratio of power applied to the coax versus the amount of power returning from the antenna due to an imperfect match. It's a rough measure of the quality of the match, but in commercial applications and strictly technical discussions is rarely used. Return loss, which is measured by frequency domain reflectometry, is the more common measure, and is quantified in decibels. FDR essentially transmits a very low power signal along a band of frequencies specified by the operator, and then measures the level of the signal that returns. By using an FDR you can see the performance of an antenna across a huge bandwidth, and never have to connect a transmitter to it. You wouldn't want to connect a transmitter up and put 1000 watts into an antenna that had a VSWR of 3 or 4 to 1. Ouch. VSWR will also only measure at one frequency at a time - so if you want to check your antenna, you would have to transmit on every frequency throughout its tuned range, and look at the VSWR. With FDR, you can sweep 200MHz in seconds, and see exactly where the antenna will perform poorly, or where it has problems. Good FDRs are priceless. You can see bad connectors, kinks in cable, water infiltration, you name it. And you can tell how far up the cable it is. Indespensible.
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As for the meter on scanners, it's just an S-Meter, or Signal Meter. It shows a relative signal strength, adjusted to some arbitrary max value that varies between models and even different units. That is to say my 780 next to Jasons may show 4 bars, and his may show 5. It just gives you a rough indication of how strong a signal is, but I wouldn't rely on it for more than curiousity reasons. It's not an indication of the quality of your antenna. A really strong signal can conceivably peg an S-Meter, even though your antenna is crap.