If it's cosmetic or superficial damage, such as from scraping a curb, the wheel is probably still round and has no bent sections or chunks of metal missing. On the other hand, if the wheel is bent, cracked or structurally weakened from hitting a massive pothole, running over a steep curb or some other mishap, it may need to be replaced, though it could possibly be repaired.
A dented wheel may not be able to maintain a seal with the tire bead, resulting in consistent slow leaks or blowouts, and will be difficult if not impossible to balance so that it doesn't vibrate at speed. A wheel with structural damage could eventually break apart. When in doubt about the severity of damage, a mechanic experienced in assessing wheel damage should inspect the entire wheel with the tire removed.
Whether to repair or replace a damaged wheel is often a judgment call, but because it involves safety issues as well as cosmetic concerns, the best course is to err on the side of safety.
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