In general, switching means it can select from multiple input sources. Even a basic receiver acts as a switch - press CD and it takes the input signal coming from the CD player and process it, press Video1 (or whatever) and it takes the input signal coming from the cable box and processes it. HDMI switching means that it can select between multiple HDMI inputs, process the signal, and send it out a single HDMI output (so you could have say a dvd player and a cable box connected to separate HDMI inputs and it can send the output of whichever one you select). If you didn't use an AV receiver and instead had two devices connected to different inputs on your TV then the TV would do the switching.
THD = Total Harmonic Distortion. The spec says that when measured across the entire frequency range of 20 - 20 kHz it can produce 350 watts, with each channel maintaining 50 watts each if all channels are active at the same time (which doesn't actually happen in practice). At that output level, the distortion level will be less than .07%, which is very good. Note though that it is a sliding scale and they could lower the distortion level by quoting a lower wattage output or conversely make it appear more powerful with a higher wattage with a slightly higher distortion level.
The 1 kHz rating is the same except that it is measured at that one frequency only. Clearly it is easier to drive one single frequency as opposed to a broad range from 20 - 20 kHz. That is why the wattage rating is higher. The 1 kHz rating is the DIN measurement standard whereas the full bandwidth measurement is the FTC standard we use in the USA.
