Base stats are the general outline of statistics for a specific Pokémon species.
Base stats usually give a general idea of the strengths and weaknesses a specific Pokémon will have. Pokémon often focus on some stats more than others. For example, Umbreon is mainly a defensive Pokémon; therefore its base stats in Attack and Special Attack are low compared to their corresponding defensive stats.
There really isn't a relationship between the two. Base stats just set a mark for where the pokemon stands in the stat. You wouldn't say (well, depending on the situation) that Mew has 236 speed. You would say it has a 100 base speed stat because the actual stat can vary upon the nature and evs.