A neutron star is usually formed when a star, like our sun, supernovas (explodes and dies). Neutron stars themselves aren’t able to explode in the same way. If there is a star near to a neutron star, then matter from that star can fall onto the neutron star, because of the strong gravitational pull. When this happens, the matter that falls onto the neutron star burns and we see this as X-rays from earth. If this continues to happen, not all of the matter burns. This causes the neutron star to become more and more compact until it collapses into a black hole.
As Emma said, neutron stars are already dead (i.e. they don’t burn fuel in their cores), so don’t explode as stars like our Sun do.
If a neutron star is in orbit about another neutron star or a black hole, then over time they will spiral into each other before colliding. In the final moments before the collision, a lot of energy is released in the form of both electromagnetic radiation (light) and gravitational waves. This happens very quickly so to us it will look pretty explosive. After colliding, we believe that either a more massive neutron star or a black hole will be formed.