The dependency graph is like a series of instructions for how to get the current scene starting from scratch: “create a sphere A, move these CVs, create a curve B, project curve B onto sphere A to create curve-on-surface C, trim sphere A using curve on surface C”, and so on.
What this lets you do is modify or reshape input objects, change attributes on a node, change node connections, or delete nodes, and have Maya automatically and instantaneously update the entire scene to reflect the changes.
You can organize nodes together using container nodes. Container nodes are a special type of node that lets you organize nodes into logical groupings for a special purpose. They can be used to simplify the view of dependency graph.