Acceptors are impurity atoms that have a one less electron in their outer orbital in comparison to the substrate material. For silicon, which has four electrons in its outer orbital, any trivalent impurity atom (such as boron) is an acceptor as they have three electrons in their outer orbitals. These acceptor atoms are added to the substrate in one of many different ways and are typically at concentration levels of 10^12 - 10^18 atoms per cubic centimeter. With this "lack" of electron, a semiconductor doped with acceptor atoms will have more holes as carriers and will yield a p-type material.
Acceptors are trivalent impurity atoms that can take an electron. They are added during the doping process to create a p-type semiconductor.
Electronic Devices : Conventional Current Version, 9th Edition by Thomas L. Floyd
The diffused impurities with three valence electrons are called acceptor atoms.
Electronic Devices and Circuit Theory, 11th Edition by Robert L. Boylestad & Louis Nashelsky