Four times the resolution of HD, or least 1440 x 2560 pixels. This is a very high resolution found in high-end flat-panel displays, including in phones.
The minimum HD resolution is 720 x 1280 pixels (commonly known as 720p.) Quad HD doubles that in each dimension, resulting in four times as many pixels across the whole area. It's the equivalent of four 720p images/displays laid out in a 2x2 grid.
Quad HD has more pixels (greater resolution) than Full HD (1080p), but not as many as 4K.
QHD should not be confused with qHD. Upper-case "Q" means quad (4x), while lower-case "q" means quarter (1/4).
Quad HD displays in phones provide extremely sharp detail, often more detail than can be seen with the naked eye at normal viewing distance. The extra detail is more obvious when the phone is used for VR, making Quad HD a desired feature in phones intended to be used for VR.