the 32, 35, 40,mm etc are the diameters of the 'slidey tube parts' of the fork, called the stanchions. In general terms, the larger the diameter of the stanchions, the more rigid the fork. But that also adds weight, so there are multiple sizes for riders' needs. Cross country or lighter duty bikes will often have 32mm stanchions. More aggressive bikes will have 34-36mm, and freeride and downhill bikes will be 35-40mm depending on the design/brand. Currently, the only two forks I can think of that are at 40mm are the Fox 40 DH fork, and the now discontinued Rockshox Totem.
I'm assuming you are rather new to the whole mountain biking sport, correct? If not, please forgive this explanation. I just assumed because of your question. If you are new to upgrading your bike, you might want to continue reading.
If you are looking to upgrade your current fork, stanchion diameter should not be a primary consideration. The most important thing is to make sure the new fork you get will fit your frame's head tube. This is called the steer tube measurement (the diameter of the tube that connects your fork to your stem and handlebars). Current forks will have either an 1_1/8" straight steer tube, or a 1_1/8"-to-1_1/2" 'tapered' steer tube. Most bikes more than 5-6 years old will have the 1_1/8" straight steer tube. If you get a fork with a tapered steer tube, but your frame has a straight 1_1/8" head tube, it won't fit your bike and you wasted your money. So make sure you know what you have in order to get something that will fit. And whatever fork you get, you may have to get a new headset and/or crown race to fit the fork to your head tube.
Next, and very important: Don't change your travel too much from what came originally with your bike. If you put a long travel fork on a bike that is designed around a short travel fork, two things go wrong: 1) you will mess up the bike's indended geometry. Long forks will make your bike 'choppered out,' having a really high front end and a low back end. That is bad for pedaling, and it can look pretty lame on a bike that was designed for shorter travel. 2) A longer fork puts a LOT more stress on your frame than a short one. Your frame was designed for a certain amount of force, and if you put a fork on that exceeds that leverage, it can snap your frame. Bad news bears. So be honest about your bike and its capabilities. There is no shame in having a shorter travel bike at all. If it is a trail bike, don't put a massive downhill fork on it. If it's a freeride bike, don't put a little xc fork on it. If your bike originally comes with, for example, a 120mm travel fork, you could probably get away with putting a 140mm travel fork on there, provided your frame can handle it, of course. Just don't put a 180mm on a bike that's designed for a 120mm. That's going way too far, and you're headed for trouble.
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