Hot Jupiter (HJ) is a term for a gas extra-solar planet the size of Jupiter or larger orbiting close to their parent star, e.g., less than half an AU. Less than .1 AU is not uncommon and extremely close ones can have very short orbital periods, i.e., their "years" can be less than an Earth day. Also, some orbit retrograde.
The term inflated gas giant is also used for such planets. Being hot, the gas expands, increasing the volume, thus decreasing the density.
Being heavy, close to the star, and having short orbital periods, hot jupiters are the easiest planets to find: the star's radial velocity is high and other signs of an exoplanet are also more pronounced.
An interesting statistic has been that the higher the metallicity of the star, the more likely it is to have a hot Jupiter, leading to theories both on their formation and on mechanisms that could bring them close to the star.