As above, they conduct on over-voltage and dissipate most of the surge energy. Their cost is partly down to quality of construction & brand-loyalty, but also how much energy the component part can absorb before it fails.
Most home only really need a Type 2 SPD, one that is rated for the rather short surge that is induced from a nearby lightning strike or a big fault / motor switching, etc.
However, if you are at the end of a long overhead line, or if your property has a lightning protection system, then you might be faced with a much larger surge from a direct hit on something conductive and so a Type 1 (or Type1+2) would be needed. They are way more expensive as they can absorb an order of magnitude greater energy.
Forget if it is 10kA or 20kA peak rated SPD, the difference between a 8us/20us shape and a 10us/350us shape is far bigger!
You can test them with an insulation tester, though some of the fancier MFT have a specific test option to do so. Basically if you check at 250V DC they should not conduct (resistance over 10M) but attempting a test at 500V (for type 2) will show quite a low IR value (well under 1M). Many IR testes show the sustained test voltage during the test, that typically would be in the 400V region.
Some Type 1 don't really show any conduction until you try at 1kV when the gas discharge tubes flash over, but that is risky to do on an installation in case something is still connected and doesn't like it!