What does Pokémon Appraisal actually tell you in Pokémon Go?

Depending on your team, the leaders say different things. This handy chart will help you determine what they're actually saying.

Appraisals are explained in depth here.

For your particular example, it means the following:

Overall, your Rainer is a wonder! What a breathtaking Pokémon!

This Pokemon's Individual Values (IVs) are at the top end (82.2%-100%)

I see that its best attribute is its Attack.

This means the Pokemon will do more damage with its moves than Vaporeons with lower Attack.

Its stats exceed my calculations. It's incredible.

Pokemon has perfect IVs in at least one base stat.

Your Rainer is tinier than any we have on record. Astounding.

Your Pokemon is small size.