Gravity
Neutron stars are the most extreme and fascinating objects known to exist in our universe: Such a star has a mass that is up to twice that of the sun but a radius of only a dozen kilometers: hence it has an enormous density, thousands of billions of times that of the densest element on Earth. An important property of neutron stars, distinguishing them from normal stars, is that their mass cannot grow without bound. Indeed, if a nonrotating star increases its mass, also its density will increase. Normally this will lead to a new equilibrium and the star can live stably in this state for thousands of years. This process, however, cannot repeat indefinitely and the accreting star will reach a mass above which no physical pressure will prevent it from collapsing to a black hole. The critical mass when this happens is called the "maximum mass" and represents an upper limit to the mass that a nonrotating neutron star can be.
However, once the maximum mass is reached, the star also has an alternative to the collapse: it can rotate. A rotating star, in fact, can support a mass larger than if it was nonrotating, simply because the additional centrifugal force can help balance the gravitational force. Also in this case, however, the star cannot be arbitrarily massive because an increase in mass must be accompanied by an increase in the rotation and there is a limit to how fast a star can rotate before breaking apart. Hence, for any neutron star, there is an absolute maximum mass and is given by the largest mass of the fastest-spinning model.
