There are three main types listed here and each has a slightly different purpose.
These brushes have been with us for years and are great with most types of brushable coatings. They are superior with oil based products, but water based products will make the natural bristles swell and it becomes harder not to leave brushmarks. For water based paint then it is best to use a synthetic brush.
These are great with water based products as the fibres do not swell as they soak in the paint. Synthetic brushes are very easy to clean and although they are in the main lovely to work with avoid the cheap ones which tend to have shorter and thicker filaments and are hard to brush out.
These come in all shapes and sizes for more specific uses - check out the sash brushes which are great for furniture painting.