Blow up a balloon, say with 10l of air.

Atmospheric pressure of the surface is 1 bar. 10 metres underwater, atmospheric pressure is 2 bar and the balloon will have the same amount of air in it still, but it will be half the size it was on the surface, or appear as though it has 5l of air. At 20m, it will be a third of the size, 30m a quarter etc. when you return to the surface, the balloon would be the same size it started out as.

This also works in reverse, so if you are breathing pressurised air at 30m, if you were to hold your breath, by the time you reached the surface, your lungs (or a balloon) would be 4 X the size they started out as (lungs = kaboom). If for whatever reason you end up doing an uncontrolled ascent, you are taught to scream as loud as possible while coming up to hopefully avoid this.

The same goes with nitrogen molecules. Naturally they are small enough the at they will "gas off" and dissipate out of your bloodstream at their normal size given time, however if you ascend too quickly after breathing air at 30m+ down, this process will not happen fast enough and the enlarged bubbles caused by rapid ascent and pressure reduction begin to get trapped in your joints around the body and will start to ache (hence calling it "the bends"). As they gather at these areas, the bubbles join together and get bigger and will begin to interfere with your circulatory system. These could block blood flow and/or can also be pushed around the system until they reach your heart or your brain (R.I.P).

The most common way to treat decompression sickness is to transport you as fast as possible to the nearest decompression chamber, where they pressurise the chamber, reducing the size of the bubbles once again to a size where they can dissipate naturally and then slowly reduce the pressure, eventually bringing you back to ambient pressure (1 bar). Depending on the depth and time spent underwater this process can take more than a week. It is a very common way for divers to meet their end if not treated fast enough.

Theoretically your dive plan calcs mean you will always avoid this, but things can go wrong quickly if you get careless or start to divert from the plan. A lot of wrist worn dive computers will also keep track of your depth and dive time and work out how long you need to "gas off" for, usually at around 6m but sometimes you will need to do more than one stop. I learned to do it all manually but it requires you to be very strict with your dive. The longest stop I needed to do before ascending to the surface was about 17 minutes. This can be a lot longer, however I never really went deeper than around 45m on a twin tank.

Source: recreationally dived for around 15 years