Definition: These are gas giants that have a similar size to Jupiter or Saturn (heavier than about 100 times the mass of Earth). They are primarily composed of hydrogen and helium.
Hot Jupiters are exo-Jupiters that are close to their stars and therefore receive a lot of energy from it (thus they are hot).
Hot Jupiters usually orbit their stars in just a few days (as opposed to one year for Earth, or even 87 days, for Mercury). They can have outside temperatures of more than 1000°C.
This type of planet is easier to observe with the transit and radial velocity method than other types, and thus were among the first to be found.
Example: 51 Pegasi b