There are two seasons in Galapagos.  The warm (also known as the wet) season and the cold (also known as the dry) season.  Remember these terms are relative as the wet season is not very wet and the cold season is not very cold.

The warm season is from the middle of December until May.
The cold season is from June until the middle of December.
The diving is excellent all year long but the 2 seasons are different.  Here are the advantages and disadvantages to each season from a diver's prospective:

Warm season
Advantages
The water is warmer and calmer.  This means less wetsuit is needed and the crossing are smoother.  The days are sunny and warm.  There are more manta rays this time of year and the hammerhead schools tend to be larger.  The land animals are more active during this time of year.
This time period also corresponds with the winter months in the US and Europe so if you are looking to escape the cold, Galapagos is a beautiful place to do it.

Disadvantage
This is not whale shark season so encounters are less common at this time of year.

Cold season
Advantage
This is whale shark season so encounters are very common at this time of year.

Disadvantages
The water is colder and the seas are rougher.  This means more wetsuit is needed and the crossing can be rough.  The hammerhead schools tend to be smaller and it is unlikely you will encounter mantas. 
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