MD5 is a cryptographic hash function that generates an 128-bit hash. Many people used to, and unfortunately still do use it to store passwords, but there are very good reasons not to. It’s not collision-resistant, and due its popularity, there are large rainbow tables available for it.
However, even without the vulnerabilities, using MD5 to store passwords is extremely unwise due to its speed. Clusters of modern GPUs can calculate hundreds of billions of MD5 hashes, meaning if your database is compromised, any MD5 hashes will be quickly cracked. Coda Hale’s article about why you should use bcrypt instead is highly recommended: How to Store a Password