The name means the man from Majrit, which is the Arabic name of Madrid, then a frontier fort rather than a city of any importance. His working life was spent at Cordoba, in the last decades of the caliphate, and the early Andalusi accounts of him describe a teacher at the centre of a circle rather than a solitary author.
His best documented work is a recension of the astronomical tables of al-Khwarizmi, adjusted to the meridian of Cordoba and converted from the Persian calendar to the Hijri. Tables are not glamorous, but they are the instrument everything else depends on, and this recension is the version through which al-Khwarizmi's astronomy eventually reached Latin Europe, since the Arabic original does not survive. He is also credited with work on Ptolemy's Planisphaerium, the treatise underlying the theory of the astrolabe, and with writing on the astrolabe itself.
What matters as much is the students. The astronomers who came out of his circle, among them Ibn al-Saffar and Ibn al-Samh, wrote the instrument treatises and tables that later travelled north through the translators, so a good deal of what Latin Europe learned about the astrolabe descends from one Cordoban classroom. He died around 1007, shortly before the civil war that ended the caliphate and scattered its scholars.