Until recently my knowledge in this area was very limited. I suppose that it still is however I've been reading, studying and have had the help of some mentors. I'll share a bit of what I think I understand or have been told.
VSWR is Voltage Standing Wave Ratio. It could be calculated with power measurements or impedance measurements.
Some meters measure the power going forward and the reflected power. Bird makes a very high quality meter (expensive too!!) that does this. You can home brew as well. You calculate SWR from the readings.
Some meters work like a bridge with three legs of the bridge being non-inductive resistors that match the impedance of interest. The load is the 4th leg of the bridge. If the load is the same (that's what you'd like) there will be no imbalance and no voltage to be measured across the bridge. A voltage indicates an imbalance. A simple version would allow nulling but no actual measurement. Better versions can be calibrated. The resistors in the bridge do consume power so you don't normally leave this in line. You probably could leave a Bird meter in line without significant losses.
If your load matches the impedance of the transmission line the VSWR will be 1:1. Measuring the VSWR at the load doesn't tell you what the transmitter or source sees - unless the load and line are a good match. Usually they aren't. Measure the VSWR at the transmitter or source.
All transmission lines have some loss. Transmission line loss actually helps keep SWR down - the more power absorbed the less reflected. While this can be of some benefit it can also confuse readings. A low VSWR might indicate a very well tuned antenna system or one that has lots of resistive losses. If you keep adding transmission line the VSWR will get better, all other things being equal.
Reflected power goes somewhere - either out the antenna or absorbed in the transmission line. Just to be clear, "out the antenna" includes the radiation of antenna and the resistive losses (those can be high too). Apparently in TV and other transmissions a high SWR can result in fuzzy images. A pulse that was supposed to leave on the first try is partially reflected back then travels back to the antenna again. The energy arrives at the receive some small but significant time later - enough to cause a problem.
A good way to begin understanding this is to just think about the behavior of a single pulse that originates at the transmitter or source. In a well matched system the pulse energy travels down the transmission line, loosing a small amount to the transmission line and is fully absorbed by the antenna or load. A dummy load is designed to behave in this way. Note that the impedance of the dummy load should match the transmission line within reason. I only mention this because the tranmission lines I play with are 50 ohms (or 52 ohms)(RG-8/9913, RG-8X, RG-58, RG-174) 75 ohms (RG-59, RG-6), 93 ohms (RG-62), 300 ohms (TV twinlead) and 450 ohms (heavier twinlead for transmitters).
Anyway, good references are ARRL or RSGB publications. Antenna handbooks are fairly abundant. Google on Smith Chart - that may yeild some good stuff.