Toilet clogs are ultimately the result of something blocking the normal water flow in the toilet. When water leaves the toilet it goes into an opening underneath the toilet. The water flow then leads to the home septic system and then ultimately to the waste extraction system of the entire local area. A clogged toilet is usually the result of a clog early on in that system and for that reason your main goal when it comes to unclogging your toilet is to remove that clog by applying as much suction as possible to the toilet bowl. If the suction is high enough it should move the clogged material enough that the water flow can take care of the rest of the unclogging procedure.
Your best weapon of choice in this endeavor is a simple toilet plunger. People will try to sell you other items that you can use and many fancy gadgets but it has been the experience of professionals in the business that most of the toilet clogs that occur can be solved with a simple toilet plunger purchased from the dollar store. If you have the black bowl plunger make sure that the inner layer is pulled outward as that will concentrate the sucking motions of the plunger. Then, place the plunger against the bottom of the toilet bowl and push forward against the resistance before pulling back once you have pushed the plunger completely against the drain in the toilet bowl. Repeat this procedure until you feel a large shift and then try flushing your toilet again.