A qari is a trained reciter of the Quran, skilled in the rules of tajwid, the exact phonetics of its recitation, and the office concerns the correct and beautiful sounding of the revelation.
The science of recitation
Tajwid is the body of rules governing the recitation of the Quran, the precise articulation of the letters, the lengths of the vowels, the points at which the voice pauses or runs on, the nasalisation and assimilation of sounds, and the qari has mastered these so as to recite the text exactly as it is held to have been given and to have been recited by the Prophet. The office is thus one of exactness in sound, preserving not only the words of the revelation but the manner of their utterance, which is regarded as part of what was transmitted.
Art and transmission
Beyond correctness, the qari cultivates the beauty of recitation, and the great reciters are celebrated across the Muslim world for the power and beauty of their voices, their recordings widely heard, so the office joins a science of exactness to a recognised art. The recitation is learned by long training under a master, ideally within a chain of transmission reaching back through the generations, and there are recognised readings, differing traditions of the recitation, that the qari may master. The office overlaps with that of the hafiz, who memorises the text, and the two are often combined, but the qari is defined specifically by the skilled and correct sounding of the Quran, the guardian of how the revelation is to be heard as much as of what it says.