I have been developing Microsoft Access databases for over 10 years.
Access is a database platform created by Microsoft, that's been around for a while now. It is used to store a set of information, query that information, build easy-to-use graphical interfaces, and create reports on the stored data.
Many business use Microsoft Access, because it is easy to maintain, and requires very little infrastructure to support. It is easy to set up tables, create forms, create queries and reports.
Microsoft Access was probably not meant to be used for some applications it's currently being used. There are many limitations to Access that the developer has to be very aware of. However, it is a great starting platform for database development - should the demands of the business increase, it is not hard to take what has been designed in Access, and re-engineer it in something more robust.
Of course you can use Access as a personal database too, to keep track of anything you want to keep track of... I have a friend that keeps track of their Coin collection in Access. I'd say if you just need to store simple information you can even use excel... but if you want to store a set of information that have relationships among components of the information, and you are interested in querying that data and creating reports from it, Access is a good option.