Can be used as an intensifier / for emphasis, or meaning 'completely' / 'thoroughly' / 'totally' combined with adjectives. Probably used only in London and parts of the South East of England.
“That was a proper good arse-kicking mate. Let's go to the pub and get a pint to celebrate.”
Note: The equivalent in the North of England is 'well', as in “We're well fucked now” meaning completely / totally / 100% fucked, i.e. in trouble / danger or we have no options after something has gone wrong. Another example (N. England only) “she was well pissed" (with stress in 'well') meaning she was very drunk. (Important: never meaning “angry" in Britain as in the US, although England does have the common “(be) pissed-off" meaning “mildly annoyed” and "Piss off!" meaning "go away!").
Proper is actually a word you can use all by itself, you can just expostulate "Proper!" and it means something similar to "Wicked!" or "Excellent!" or "Cool!". It is an exclamative word. If something totally cool or awesome happens you just say "Proper!" and it means the same as "Awesome!" or "Cool!", but it is much newer and fresher and better and longer-lasting than those words. Its literal definition is "Perfect". Say this if you want to not only be with it, but way, way ahead of it. Proper.