Access is relational database program. It has full Visual Basic capability embedded into it so that it not only manages data, it can be used to design applications to link, collect, analyze, and report on data. Because it is relational, a database that is properly designed can maintain links or join relationships between various data from different sources or from various levels of data. Microsoft Access is at it best in a local environment (personal database) office application. That being said, Access can work reasonably well in a multi-user environment for small and medium size businesses. One approach is to split your database so that the data resides in a separate data-only database on a network, and users run local copies of the database (which contains all the design) with links to the "data" database. This minimizes design corruption that can sometimes occur over a network. Access has reasonable multi-level security controls albeit they take some getting used to. Newer versions of Access have a security wizard that helps with most aspects of securing a database.
As to the type of data, virtually anything you can do with Excel you might be able to do more efficiently with Access. The downside of Access is a bit of a learning curve but once you get your tables, queries, forms, and reports set up the way you want them - the design is controlled and your data updating/reporting will be simplified.
Have you ever had a chart or graph in Excel that you had to go back to update data ranges all the time? That's what Access can eliminate because it always crunches through all available data automatically. Reports and charts update any time based on new data entered. Actually the line between Excel and Access is a bit blurry. Excel can do database type things like forms, cell (data) validation, pivot tables, and queries (with mutliple data sources) thru MS Query. Similarly, Access is capable of almost all the calculations that Excel does - only the functions are embedded into queries, unbound fields in forms & reports, or VB code. Access can easily handle tens of thousands of records and related data if data is structured properly. Access easily handles data relationships and type, and full-blown reliable applications such as billing data, etc are possible IF you have somebody that knows database structure and VB code.
In summary, for thousands of records of business and time critical data with multiple users, you probably need to be at least considering a server-class database like Oracle for reliability and server class performance. If number of users is small, and if some downtime is tolerable (in case you need to recover from a corrupt database), and if your data is dynamic (in other words Excel becomes cumbersome) then Access is a really useful option.
Hope this answers your question which I think is about what kinds of things Access can do for you.