I work as an Access & Excel progammer where I create lots of customised Access databases and Excel spreadsheets.
Generally Excel is great for creating charts and doing calculations. Access is a database and a good way of organising your data, and provides an easy way to query your data. Here are the differences (generally)
Access
++++++
First theres a lot more to learn (compared to Excel)
Lots of people can look at your access database at once. If one person makes a change to the data, everyone will see the change.
Your data is centralised and stored in tables
You can query the data (eg for a mumsnet database you could find out mumsnetter will more than 2 children, or children over a certain age).
You can produce customised reports
You can export the data (either from tables or queries), to Excel, Word, or plain text
You can also bring in data from Excel or text files or even other databases
Through the use of forms (ie screens), you can determine what data you want to see. In this way sensitive data can be hidden from view.
Also when people update the database, Access can validate the data (eg make sure the data entered is correct and not due to typing errors, or out of a particular range).
Excel
+++++
Only one person can update a spreadsheet at a time.
There is a danger of creating lots of spreadsheets about the same thing. Eg If we created a new spreadsheet for every new project we started, and then say the project manager name changed, then you would have to go through each of those spreadsheets and change the name. This has a real danger potential as some spreadsheets may inadvertantly not be updated, and then you'd have a discrepency in the data ! In Access (if the database is set up properly), you would change the project manager name once, and this would be reflected across all projects.
Hiding data is not as secure as Access
Validating data again is not as good as Access
Good for creating charts, what-if scenerios etc
This is really just the tip of the iceberg. If you have any specific questions I'll be happy to help. FWIW there are loads of introductory books to Access around - you should find one in your local library. However you only need to read these books if you are planning to set up a database or if you plan on doing your own queries and forms. The Access databases I produce for my users have no knowledge of Access at all but mearly press the relevant buttons to run reports, run in data and see specific results. HTH