Generally, there are two types of paint brushes, those made of natural-hair bristles and those made with synthetic materials (usually nylon or polyester).
Natural bristle brushes are preferred for use with solvent-based (oil- or alkyd-based) paints, especially for enamel or finish work. Natural bristles are hollow and can absorb the water contained in a latex paint, causing them to swell and become soft and limp (similar to your own hair when it is wet).
Most synthetic brushes work well with both latex and solvent-based paints, but always check the manufacturer’s recommendations on the brush. Some of the solvents used in solvent-based paints can break-down the compensation of a synthetic bristle-once again check the label.
Keep in mind, the same above rules apply to roller covers: synthetic vs. natural (wool).