The Gas Compressor ability is used in The Sun biome. The Sun can be unlocked when you reach Prestige 5.
To use the Gas Compressor, you must do the following:

1. Equip the Gas Compressor ability
2. Enter the Sun Biome
3. Tap on the Gas Compressor ability
Each time you tap it, it fills it by +25%, 4 times in total to reach 100%

4. When you reach 100%, it will drop +10 Hydrogen by default without any modifications
Hydrogen can be used for crafting QBit, Dyson Sphere Part, and Quantum Chip.