What does 'fully determines' mean in the context of postgres functional dependency statistics?
It means that if col1 is identical for two rows, then col2 will also be identical.

In other words, if the functional dependency were perfect, you could remove col2 from the table and use a lookup table that maps col1 to col2. But don't forget that these are only statistical data from a sample of the rows, so even if you see a dependency of 1 in the extended statistics, that is no proof that it is really always so (only very often).