Microsoft Access is a popular and relatively inexpensive database system. It's easy to learn, and powerful enough for everything but the largest enterprise applications.
It's All Relative
Microsoft Access is an RDBMS, or "Relational Database Management System." Any database stores information in tables. With a Relational database like Access, "related" data is stored in many separate tables and linked together. For example, one table in the database might contain a list of customers, while another table might list the orders any customer has made. The link between those two tables would be a customer number that appears in both.
One other important factor in databases is Normalization. The key thoughts behind normalization are that similar data is stored in the same place, and the same information is never stored in two separate places. A database that isn't normalized is harder to search. A "Name" field can hold different versions of the same name: "John Z. Smith," "JZ Smith," "John Smith," and "Smith, John Z." All of these names are the same person, but since they're all stored differently, a database search will not be able to find them all. A Normalized database, on the other hand, will split out the parts into their own fields--Last Name, First Name, Middle Initial--so that every name is stored in the same way.
Tying it all together: SQL
SQL stands for "Structured Query Language." SQL is the set of commands Access uses to search through the records in the database. Here's an example of SQL code: SELECT OrderNumber, Quantity, Price FROM Orders WHERE CustomerNumber = 12345 This program, or "query," will pull up all of the orders sent to this particular customer. More complex queries use the relational links to pull in data from any table in the database.