There's 2 things you need to know:
- the damaged item in your picture is a bumper cover, it's plastic, it's only job is to make the back of your car look pretty. If you take it off, you can bend it and twist it with your bare hands.
- the actual bumper is a horizontal steel beam behind it, usually with styrofoam/polystyrene on it. It's heavy, it's job is to absorb hits.
As has been pointed out by others, the only thing we can say for sure is your bumper cover is bent inward. The only way to know if the actual bumper is damaged, bent, twisted or needing reinforcement is to look at it. The easiest way is to take the bumper cover off, but in your case, I would suggest that your bumper is most likely perfectly fine, as your bumper cover is bent above where you would expect the bumper to be.
Here's your options:
- Fix that bumper cover in place: this may be easier than you think, as you may be able to get your hands behind that section that's pushed in if you get at it from underneath. Push it out if you can, preferably with your bare hands. Be careful not to detach the bumper cover by accident. I would push outward with one hand, and pull the bumper cover towards the car with my other hand, or ask a second person.
- If that doesn't work, try removing the bumper cover. Get under the back of the car and look for little screws holding it onto the actual bumper. Modern cars are likely to be using little plastic clips that love to break. Some Japanese cars have this nifty little setup where the bumper and bumper cover slide right off the car just by removing a few bolts at the bottom of the trunk. Lift up the carpet or spare tire cover and look around. However you do it, once the bumper cover is separated from the bumper, you can use more force to push that bent section back out.
- Replace the bumper cover: junkyards are your cheapast option, and you should be able to find one in your exact colour. If not, there's aftermarket bumper covers to be bought (not at the dealership), last place to look is the dealership. The thing about new bumper covers is that usually they are not painted. Go to a hardware store in the spraypaint aisle, find the colour match for your car. They often have a booklet where they list which spraypaint colour matches the year and make of your car.
- Get the bumper cover replaced at a shop: this is your most expensive option.