The Aquanauts mined and collected the crystals for survival. They used submarines and other vehicles to collect the crystals (and fight off opposing Aquasharks) and bring them back to their base, the Neptune Discovery Lab.
It is unclear if the crystals were used to power their vehicles, or if they were used for trade. Later Aquazone subthemes like the Hydronauts and Stingrays has similar motives. Later themes, like Rock Raiders, have much more detailed mythology and background story that give us further insight regarding the purpose of the crystals.
For the Rock Raiders, based on the video game and promotional materials, the crystals represented the only source of power for the stranded crew. The crew crash landed on the mysterious planet, and they had to collect crystals to power and repair their vehicles to eventually make their escape.
The Rock Raiders, and later the Power Miners, battled native rock monsters to obtain the necessary crystals. According to Power Miners mythos they were sent down to investigate the source of recent earthquakes. They discovered that the rock monsters were creating the earthquakes, and that the rock monsters consumed the power crystals as a source of energy. The obvious solution was to take away their source of food, causing the rock monsters to starve and die off.
In more recent Town, Lone Ranger, and Superheroes sets the pearl gold and silver crystal appears as a source of valuable wealth, basically gold.
The recent announcement of a new Arctic theme provided us with a few images of the new sets, which include crystals in the blocks of ice. At this point it is unknown if the crystals have value, are a source of power, or are merely ice.