Maven uses a Project Object Model to describe a project. This includes definitions of the dependencies and executions to use for a project, the reports to run when building, and a host of other features. In Maven 2 that model is defined in the pom.xml (in Maven 1 the file was called project.xml).
Maven expects to find the pom.xml in the root directory of the project (though this can be overridden). When you run a Maven goal, the POM is parsed from pom.xml, Maven determines what dependencies and plugins are needed, downloading them from the remote repositories, then runs the plugins that are configured for the project.
For a jar project, running mvn install will by default perform a series of operations based on the default lifecycle bindings. You can define additional operations by adding plugin definitions to the pom and binding them to the relevant phase of the lifecycle.
The Maven book is a good guide to Maven. The Maven by Example section will walk you through the various parts of Maven configuration.
If you are familiar with Ant, have a look at the Comparing Maven with Ant section to understand the differences.