Students are taxed in exactly the same way as everyone else. Everyone is allowed to earn up to �5035 (in the current tax year) without paying any tax. Students who only work during the vacations don't normally earn this much, so they don't pay any tax.
After your earnings pass �5035, the tax man will take 10p out of of each extra pound. This continues until your earnings reach �7185. Thereafter, the tax man takes 22p from every pound. (If your total earnings in the tax year exceed �38335, the tax man will take 40p out of every extra pound).
Obviously, it would be daft if people actually didn't pay any tax for the first few months of the year but had to pay a lot at the end ofthe year, so the PAYE system averages the tax out across the year.
Chris