A garlic press is used to crush garlic cloves efficiently by forcing them through a grid of small holes. This gives a convenient alternative to mincing garlic with a knife, especially as the clove may be passed through the press without even removing its peel; the tough skin remains in the press while the garlic is extruded out.
However, it's worth bearing mind that minced garlic has a different flavour to chopped garlic; more cell walls are broken, resulting in the release of more of the garlic's strong flavour compounds. Some chefs prefer the flavour, whilst others find it inferior.
When buying a garlic press, choose a sturdy model with a fairly coarse mesh, and look for one which comes with a matching grid of blunt pins to clean out the holes.