This is simply the generic use of genjutsu as employed by Sharingan wielders. By establishing direct eye contact with the intended opponents, the user can lock them within a genjutsu of their choosing in order to achieve various effects. These effects range from inducing instantaneous, but temporary, unconsciousness in an opponent to forcefully extract any valuable information that they possess controlling their actions or to show memories.
Using his Sharingan, Sasuke stares at his opponent directly in the eyes and they stare back. Then a shadowy figure of himself appears before them forcing them under a genjutsu. An image resembling his Susanoo appears in front of the opponent and grasps them as it begins "assimilating" them into itself. This breaks the opponent's will. Afterwards, the opponent is left incapacitated.
Itachi is seen using an illusion that traps the victim in a dark empty space where their body is made of paper that burns from toe to head while the user is watching. The genjutsu will make it harder for the target to move properly. It bears a great resemblance to his Tsukuyomi, though it is used with the regular Sharingan.
Kakashi could use the Sharingan to hypnotise the target, making them make seals at the same time as he did, thus giving the illusion he could see into the future. He was also able to put multiple people to sleep with a single glance with his Sharingan, even shinobi of Anbu calibre.
Shisui was able to render people unconscious with a single glance from long distance with his Sharingan.
Madara's usage could control the tailed beasts like Kurama, or paralyse a shinobi with a single glance.
Sasuke was able to use it to undo a genjutsu Kabuto cast on Itachi.
When Sasuke used this genjutsu, he was seen covering his left eye in apparent pain afterwards.
Sasuke's completed version of Susanoo was first seen in this genjutsu, though as a shadowy figure before its complete début in the fight against Danzō.
Madara had to de-activate his Rinnegan to use this technique unlike other Sharingan techniques which can be used while the Rinnegan is activated.