Monism is the school of thought that all existence is universally one thing, which is "that which exists." Sounds circular, but philosophy at its "Philosophy for Idiots" level often does.
There are three views of existence. Monism: all things that exist are of one substance. Dualism: All things that exist are of two substances. Pluralism: there are many substances.
Perhaps the most famous advocate of monism is Baruch Spinoza. Spinoza, a self-proclaimed pantheist, believed all things are god, and that when we look at nature and study nature, we are actually seeing god itself. God is not a transcendent substance, but is understood as all that is created and existent.
 In religion
From a religious perspective, monism is often a crucial part of pantheism and panentheism, since all things are god, means all things are ultimately the same (pantheism)... and if all things contain god, then they are made of the same substance (Pantheism).
Most mystical religions or mystical aspects of religion are monistic. Writers frequently speak of "being one with all things," and finding the moment when "the links between individual entities breaks down."
Hinduism, in the Rig Vedas, speaks of God creating the world out of his own existence, and being himself in its existence. Philosophical Buddhism states that the truest existence is "non existence," becoming one with all things, as part of the universe. It is often described as letting your body, mind, and soul separate into the very matter that composes it, and letting that matter disperse into all things. Slowly, as the matter disperses, one becomes part of each tree, each cloud, each wave of water.
Even science could be said to be monistic, in that all of the universe is created of atoms and smaller particles, and that in a very real way, the individual elements and atoms which make up your body this moment are being replaced with other atoms and other elements.