Dualism can be characterized in various ways; on one account, it is simply the view that MentalEvents and PhysicalEvents are totally different kinds of events.
The most common variety of dualism is DualisticInteractionism. This seems to be the CommonSense view of the mind. But there is a puzzle about how the mind and body interact causally, and this puzzle is more serious than might appear at first. See DualisticInteractionism for details.
The other kinds of dualism also accept that mental events and physical events both exist and that they are totally different kinds of events; but unlike interactionism, they deny that mental and physical events causally interact.
According to a theory called ParallelIsm, mental events and physical events are perfectly coordinated, it is said, by God; so that when a mental event such as Sally's decision to walk across the room occurs, then it just so happens that Sally's body heads across the room. But there is no cause-effect relation between mind and body; mental and physical events are just perfectly coordinated, in advance, by God. This is view closely associated with GottfriedLeibniz.
A third kind of dualism, called EpiphenomenalIsm, has it that physical events have mental effects, but mental events have no physical effects. In other words, the causal interaction goes only one way, from physical to mental. So if Pierre eats a candy bar and experience pleasure, that pleasure is caused by his eating the candy bar; but if he decides to get another candy bar, his decision does not cause his body to get another candy bar. So mental events are just side-effects, or by-products, of physical processes in my nervous system. (The word epiphenomenon means, roughly, "by-product." That is why the view is called "epiphenomenalism"; it is the view that the mental is just a by-product of the physical.)