In the Star Wars universe, the Jedi "mind trick" is a wide class of abilities split more or less into two categories of affect mind and alter mind. These mind tricks allow Force-sensitives to temporarily or permanently confuse or cloud the minds of others for a certain purpose.
The most well-known examples of the Mind Trick in the Star Wars movies were Obi-wan Kenobi affecting the stormtrooper to pass through their checkpoint--"These aren't the droids you're looking for!" and Jabba's booming "That old Jedi mind trick won't work on me, boy!"
Like most Jedi abilities, it is to some degree genetic as to how skilled one is at mind skills. The Halcyon line, for example, possessed great aptitude for affect mind. Luke Skywalker himself was never particularly good at it, at least in comparison to his other abilities.
It takes great force of will to use this skill. Generally it only works on targets who are weaker-minded than the wielder and those without a particularly strong sense of self and will. Those with very scientific, quick minds often will see through the trick quickly. Those slower on the uptake, those distracted by something, and those with unclear beliefs and thoughts almost always fall for them. However, there are exceptions to the rule because some species, such as the Hutts, are genetically immune to these affects, no matter how smart or stupid the individual.
The affect mind skills are the more common and more acceptable of the two types. These allow the user to temporarily muddle the perceptions or senses of another. All senses can be affected. A flower may suddenly smell like garbage. The person may hear something that was not there (as Obi-wan did on the first Death Star). They may see something that never happened, either out of the corner of the eye or, with greater effort, actual objects that are not there. It's always useful, though, to give non-Jedi friends a hand--you can show them what a different hair color would look like on them without ever touching a bottle of dye. Short-term memory can also be affected, certain centers of the brain repressed. People can be made to forget seeing you, or misremember a command, or mishear a conversation for just long enough for it to pass out of their short-term and be ignored by their long-term memory.
Alter mind skills are more serious and often considered much more Dark-side skills than their 'lighter' siblings. These permanently affect longterm memory and can essentially trigger Force-based brain damage. One of the more dramatic instances of this was when Kyp Durron, under the influence of Exar Kun, erased large chunks of the memory of the scientist Qwi Xux.