There is an age that is called the 'State Pension age', and this marks the date from which you can claim the pension. Literally people who are able to claim the pension are called 'pensioners' and although it used to have negative connotations with an ageing population this is less and less the case now.
For men, the pensionable age is 65. For women it is 60. This is ironic in the sense that women will tend to live longer than men, and so to redress the balance things will change in the future.
Here are the changes that are currently scheduled to take place: Between 2010 and 2020, the pensionable age for women will move to 65 also to be in line with men. The next change will be an increase from 65 to 68 between 2024 and 2046 - so starting to look a long way into the future - and this will reflect that people are living longer than ever and that trend is expected to stay the same in the future given our ever growing level of sophistication with technology.
In order to get the state pension you need to have what are called qualifying years - these are tax years in which you have paid, or have been credited with, or even treated as having paid, the appropriate level of national insurance contributions.
As for claiming the state pension, this does not have to occur the second that you reach the state pension age. Rather, you can get it later and therefore get a larger amount pro rata, and in fact there is also the option of getting a one off lump sum amount which is taxable.