A friend recently asked me about the symbolism of keys. They come in all shapes and sizes, and they've been around since fairly ancient times.
Both physically and magically, a key can both unlock and lock things. This ability to be on both sides of the same argument is sometimes called 'antagonistic' and you come across it quite a bit in magic. You can see it in the saying 'under lock and key', which when you think about it is rather overstating things; why not just 'under lock,' or 'under key'? But the presence of lock AND key shows the antagonistic side of keys... we turn the key in the lock one way, and deprive someone of their liberty. Turn it the other way and we set them free. The lock doesn't work without its key, and vice versa.
The Roman god Janus (the month January is named after him) was, amongst other things, a good of doors and beginnings, and was often shown holding a staff and a key.
In Christianity the iconography of the key is almost always associated with the Apostle Peter, since he was supposed to be the keeper of the gates of heaven. Sometimes the key is shown in double form.
In the same way, when young people celebrate their 21st birthday they are often given a symbolic key 'the key of the door' although what door exactly is rarely ever specified. What I think it means is that when they reach 21 they used to be considered an adult - and the key symbolised their newfound power to access the world of adults and all that it entails. At least, that's my theory!
This might also explain why keys can symbolise being initiated - the key gives you access to knowledge that was previously hidden. So when we say something like, 'The key to inner happiness...' (or winning the lottery, or the key to success) we're unconsciously drawing on the key symbolising arcane knowledge.
And knowledge is power.