Wetsuit thickness is all about numbers. You'll hear straight numbers like 3 mil or 6 mil. Or you'll here something like "my suit is a 3/2".
What do these numbers mean?
It's not really a big mystery. Mils is shorthand speak for millimeters.
A 6 mil suit has neoprene that's 6 millimeters(mm) thick.
The most common scuba wetsuit thicknesses you'll see are 3mm, 5mm and 7mm.
The thicker the wetsuit the warmer it'll be.
Buy the right thickness wetsuit for the type of water you'll be diving.
Don't buy a 3mm wetsuit to dive in the North Atlantic, you'll freeze. On the other hand don't buy a 7mm suit to dive in the Caribbean, you'll likely overheat and dehydrate.
Something you'll see a lot of are multi-thickness suits. If someone starts talking about 5/3's or 3/2's this is what they are referring to.
What it means is that the torso of the suit is 5mm thick and the legs and arms are 3mm. The first number is always torso thickness and the second the extremities.
The reason manufacturers do this is to keep you warmer over the center of the body and provide freedom of movement in the arms and legs.
Be aware when buying older scuba wetsuits that over time the neoprene will crush lessening the suits ability to keep you warm.
Also take care in packing your gear. Don't put your wetsuit at the bottom of your bag. All that weight will do is crush down the suit. It could even put permanent creases in the suit. Anywhere you have a crease the wetsuit thickness will be less.
When buying wetsuits it's easiest to talk to other divers in your area and see what thickness suits they're wearing. You'll find that most people will gravitate towards the same thing for any given area.