A fuse is an electronic component that protects a circuit by creating an open circuit if it draws too much current. **Fuses do not protect against voltages that are too high. **
Fuses are most useful around power supplies, both when power comes into a system and on individual power rails. For example, if you have a 12V rail that should only draw 750 mA and a 5V rail that should only draw 400 mA, you might put a 750 mA fuse in series with the 12V supply output and a 500 mA fuse in series with the 5V supply output.
A common mistake that fuses protect against is accidentally shorting the power rail to ground (e.g., with a DMM probe as you are trying to touch the correct pins). This causes an infinite amount of power to be drawn from the power supply, and can sometimes damage or destroy voltage regulators or power supplies.
Standard fuses contain a small piece of wire made of an alloy that melts readily. If the current gets too high, it burns out and opens the circuit. Standard fuses come in many different shapes and sizes.
Resettable PTC fuses are tripped by heat caused by current above the rating of the fuse. If the current flowing through the fuse goes above its rating, the fuse changes from having very low resistance to having a high resistance (thereby stopping the flow of current through the circuit). It is self-resetting after power is removed and the fuse cools.
Circuit breakers are typically used in AC power applications like homes.