A stand (スタンド sutando) is a supernatural power. When first presented, the kanji used is 幽波紋 yuuhamon with スタンド over it; it means ghostly ripple and it is similar to ripple.
The concept of "Stand" (a contraction of the phrase "one who stands by me") was introduced in part 3 of the manga series. According to Joseph Joestar, it is the manifestation of an individual's innate power over the "ripple" (hamon) and represents, to an extent, the individual's psyche. In fact, Joseph once referred to it in the manga as the "ghost ripple" (quite apt, as most of them take on humanoid forms and hover around the wielders like wraiths). Stands are usually sustained by breathing, and hover behind and above the user while usually being invisible to non-stand users. Most Stand Users can access the "senses" of their Stands, seeing and hearing whatever their Stands can.
To people without the power of the Stand, who normally cannot see them, the activities of the Stands are comparable to ghostly and poltergeist activity, and ESP. This behavior is evidently seen in the JoJo OVA; Jotaro imprisons himself, takes a gun from the guard, aims it to his head, and pulls the trigger of the gun. His Stand's hands caught the bullet before it reaches his head. For the normal people around him, it would appear that the bullet is suspended in midair, and as a result, the other prisoners near his cell and even the guards feared Jotaro.
In general, only those with unusually strong spiritual power and determination (but not limited to human beings) can develop stands, as they are typically a reflection of the wielder's spirit. Stands can be developed hereditarily or artificially (through the Bow and Arrow). An interesting trend regarding Stands is that in their earlier appearances in parts 3 and 4 had a more humanoid appearance and mostly elemental powers, but later appearances in parts 5 and 6 had Stands taking on a more mechanical look and have more physical and intricate abilities (like controlling gravity, for example).
Although stands manifests from the wielder's psyche, some abilities cannot be controlled and may even restrict the wielder (e.g, Superfly). Though most stands acts at the wielder's will, some stands are "automatic" and the wielders cannot keep track of their actions (e.g, Black Sabbath).
It is interesting to note that the stands began to take on names of distinguished bands and album titles starting from part 4 of the series. Most of them are progressive rock bands, as Araki himself is a fan of this music genre. In part 3 some Stands are named after tarot cards, and later after Egyptian gods. In the subsequent series, some are even named after fashion labels.
Despite their power, Stands hold one drawback; any damage the Stand receives is transmitted to its user (i.e. if a Stand's leg were to be ripped off, the Stand's user will have his or her leg severed as well). This has served as a way for defeating most of the encountered opponents throughout the series, though some Stands are immune to this factor.
The greatest utilization of stand allows user to infuse the summoned Stand with their whole body. It gives them a non-negligible boost in power and speed. This however puts a great deal of stress on the body and thus requires a high degree of training to maintain. Skilled users are even able to maintain their heightened abilities while utilizing their stands special abilities.