Headphone jack not working properly

First you should check another set of headphones, just to rule that out.

Then you are looking at 2 possibilities. You may have some dirt or corrosion or something stuck inside the headphone jack. Try cleaning it out with either air, or some alcohol to try and clear it out. If it still doesn't work, then you will have to replace the headphone jack. It involves soldering on a cable, that has a lot of small soldering points, so unless you are comfortable doing that, you may have to pay someone to do it for you.