Niantic Labs created this Appraisal feature to find out approximate CP and IV values within Pokémon Go so players don't need to leave the game to open a third-party app. Personally, I think this is fantastic! Each Team Leader will have their own set of phrases, which fall into four categories: Great, Good, Decent, and Poor.
Appraisals tell you which of its HP, Attack, and Defense stat the Pokémon performs well...of four categories. Remember that IVs each rank out of 15. Although a Pokémon could rank 'Great' overall, it could then suffer in one of the three stats or move sets that make a Pokémon IV% drop.
The Appraisal is a very handy way to know at a glance whether you have a 'Great' Pokémon on your hands. Once you learn the Appraisal for your team, you'll notice these phrases are specific enough to give you a good feel for the Pokémon's strengths. If it is vague to you, then you should do more research before investing your Stardust and Candy. Remember, the overall 'Great' phrase means it's between 82% and 100% of its potential!
Generally, most Trainers evolve the high-IV Pokémon before spending Stardust to Power Up and increase its Level. EACH time a Pokémon evolves its move set IS randomized, although IVs stay the same. Consider that you may have a perfect Snorlax, but it is possibly for it to have crappy move sets that spoil all the time and work you put into it.