This idiom is used when the only option available to you is an unpleasant one, and you have no choice but to take it. The German equivalent is in den sauren Apfel beißen
For example, if you are very afraid of dentists, but have been suffering from a toothache for several days, it is high time to bite the bullet (directly translated: auf die Kugel beißen) and make an appointment.
The origin of this idiom is rather grim. Before the invention of an effective anaesthetic, injured soldiers would bite on something – for example a bullet – to help them deal with the pain of having an arm or leg amputated. It was very unpleasant, but the only option to save their lives.