There are a number of reasons why your toilet may not flush, even with a plunger. The most common reason is that there is an obstruction in the toilet bowl or trap that is preventing water from flowing through. This can be caused by anything from a build-up of toilet paper or waste to a foreign object that has become lodged in the pipes. If you suspect that there is an obstruction, the best course of action is to call a plumber to clear it for you.
Another possibility is that the flushing mechanism itself is defective. In this case, you will likely need to replace the entire unit. This is generally not a do-it-yourself job and will require the help of a professional.
Lastly, if your toilet won't flush and there doesn't seem to be any obvious reason why, it could be due to low water pressure. This can often be resolved by simply adjusting the water pressure valve on your main water line. However, if you're not comfortable doing this yourself, you'll need to call a plumber or handyman to take care of it for you.