An Access database is a database. Anything that's used to store information in a structural way is a database. Whether it's flat (stored in a file), hierarchical, network, object, or the most, popular relational, it's a database; they're all forms of storing data.
What's better? Well, Access is designed to function as a desktop application for a single user to store information. It's possible, however, to have multiple connections to it, but I wouldn't recommend it. The more connections you have to it, the more it slows it down (more severe than MySQL), and the higher the chances of data corruption (you could have multiple people modify a field in the table at the same time, and information may be overwritten; so you'd have to have some sort of locking mechanism to prevent this). I only recommend Access for personal use because it provides tools for reporting and easy data retrieval and insertion.
If you're going to create an application where multiple users have to retrieve data, I suggest you go with MySQL. Because it's a database server, it's ready to deal with multiple users. It handles locking and data corruption. It's fast too. It has security features, among other things. Also, it's free for non-corporate use, unlike Access.