It is probably the case that you have already had a passport, as a parent probably did it when you were younger so you are probably looking to renew this, as they expire after 5 years for under 15 year olds.
You will need a passport to travel out of the country and it can also be used as a form of identification too, if you are under 16 you will still need to apply for a childs passport and probably your parent or guardian will do this for you, but if you are 16 you will need to get an adult passport which will last for 10 years. It isn't difficult to do, although there is quite a bit of paperwork and you will need to get 2 passport pictures taken and I think you need to get one of them signed but you can find out more on the Gov.uk website, as this allows you to fill the form in online or you can pick one up from the Post Office.
The Post Office does a check and send service, which you can use to make sure everything is right before sending it off, there is a charge of £9.75 for this service though but it should guarantee that this goes through. If you decide not to use this then make sure you double check your form and photos before sending it off so that it gets processed and doesn't come back to you.
If you have any questions about the form, you can ask at the Post Office, or check with a parent/guardian or teacher who will be able to help.
Make sure you leave enough time to apply for your passport and for it to be processed, it normally takes up to 3 weeks (but could take longer in busy periods, like before summer holidays)