I would put some scientific explanation here as well because i was very skeptic about this subject as many say it's useless and did some deep research to find out what is really up with this thing and when/where is it good for. This is what i found out and how i explained it for myself.
How Nitrogen differs from air(consisting of 73% of nitrogen) - Air has Hydrogen in it, in low quantity though, but still.
Now the big difference comes into play in moist and/or hot climate, as condensation water accumulates in compression tanks, it does so in your tires as well. In extreme cases tire techs have even found bucket of water in a tire used for 4 years after taking off from a rim(figuratively speaking).
This water or moisture(depending how long and much there are in your tire) is the main concern, this is what makes tires heat up more slowly, unevenly, change pressure big time with temp changes or even unbalance your tire going sub zero temps(READ: minus temps in C).
So you will have biggest benefits using Nitrogen in your tires when you live in England, where it rains every other day
And least benefit in eg Egypt or somewhere in middle of desert on a sunny dry day.
gains from nitrogen
*even and very fast warm up for tires
*even wear
*more stable pressure through out very big ambient temp changes(example from +30C to -20C)
*and debatable but possible, scientist say that because of Nitrogen molecule being bigger, it doesn't escape the tire from microscopical holes in rubber form so fast than Oxygen does.