Welcome to Android Central forums. It's a giant hole in something that you keep in a pocket or a purse. There is a better than not chance that there is debris in the jack/port. If the headphone plug doesn't make contact with the bottom of the port it won't register, or work for that matter. The tip is usually the Common connection, then each segment has a different function, I'll post a diagram.
You could try just turning it upside down and tapping it on the top/bottom, whatever is pointed up when the jack is pointed down, to see if the debris will fall out but if you've been trying again and again to put the plug in it you may have mashed it in too well for it to just fall out. You could try compressed air to blow it out, but be careful that you're blowing down the side of the port so that air flow can lift it out of there. Don't just poke it in and blow, that will only hold it to the bottom of the port and not remove anything. If your eyes are better than mine you can probably look in the hole with a pen light and see the debris but be careful if you try to fish it out. Rubbing the sides or being rough can damage the internals and even if you get it out there could be other damage. If it were me and tapping and blowing didn't work, would use a toothpick and gently stir the bottom like a witches brew, it's October, and then try turning it over and seeing if it just falls out. Again be very careful sticking things in there.
Let us know what you find.