Whenever you're outside your Base, your Oxygen (O2) meter will begin to drop. When the O2 meter reaches zero, your Health will begin to drop (bottom right corner of your HUD). When your Health nears zero, you'll you begin to suffocate (the screen will begin to flash red, indicating that you are struggling to breathe). When your Health reaches zero, you die. To replenish your O2, re-enter your Base and wait for your O2 meter to refill.
Note that if you have built a vehicle, your vehicle will have it's own O2 supply that you will breathe from before you use up your suit's oxygen.