The terms you are using is all the stuff I don't understand...I know 140mm is something to do with the movement in the fork but not quite sure how that relates to the terrain you want to travel.
As PaulF said, it's the maximum travel you get from the fork. It can all get very complicated with different wheel sizes, different travel forks (some are dual position, some can be internally changed) either air or coil springs, different geometry and so on and so on...
This is very, very generally: bikes sold with forks from 80-120mm travel will be aimed at cross-country riders. They'll have a more forward geometry which will work well going up hill and on the flats but can feel like you are going to go over the bars easier when it gets steep downhill. The geometry of the frame is designed to enhance these characteristics and these are the kind of bikes you would see used in the XC races in the Olympics/Commonwealths etc. They work very well for people who want a bike to commute on as well as ride trails and they'll handle all of the graded trail runs in the UK fine.
Bikes sold with 140-160mm travel forks are usually referred to as trail/all-mountain/enduro bikes. The longer travel means they are more able to soak up big hits if you are dropping off steep stuff, doing some jumps etc. Again, the geometry of the frame usually reflects this and you'll find they have a steeper head angle which makes them feel more confident on steep descents but are harder to pedal up hill (more likely to wheelie). Many 160mm bikes use dual position forks so you get the benefits of both. These bikes can be used to commute but they're not great for it, but they'll hammer round trails like anything and take you off-piste and even down some downhill runs if you fancy it. If you want a mountain bike that'll do anything these are the ones to look at in my opinion.
Bikes sold with 170mm+ travel are almost always full-suss and over 180 is usually a downhill bike. Downhill bikes are designed for just that, hammering downhill. You do not want to pedal one up! You can get some 170mm travel all-mountain bikes and these will climb fine (FS can be designed in a way to make them climb well) but again, they're likely to be full-suss bikes that you wouldn't want to pedal on long, less taxing rides.
For me 140mm travel sits right in the sweet spot between rideable all day and able to point it down hill and feel confident. Of course, the frame matters just as much as the fork, but frames are designed with the travel in mind as I said.
I've actually just ordered a dual position fork for my BFe which runs at 130mm and 160mm. It'll probably spend most of it's time at 130 to be honest.