These buttons have been organized into tabs respective to specific workflows. Choosing a tab displays shelf items in that tab. By clicking a button on the shelf, you can execute commands or launch tools without having to choose them from a menu.
As you become more experienced in Maya, you will no doubt want to customize your shelf with tools or commands that execute custom settings. If you find that a command or tool is available from the menu bar but is not on a shelf, you can add it to the shelf.
Hold down SHIFT-CTRL and then select the command or tool that you want to add from the menu in the menu bar. As soon as you release the mouse button, the item you selected will be added to the shelf. You can quickly delete any shelf button by pressing the middle mouse button (MMB) and dragging the shelf button to the trashcan icon in the upper-right corner of the shelf.
You can create a new shelf, delete the currently selected shelf, load a shelf from your hard disk, or open the Shelf Editor by clicking the little black arrow to the left of the shelf. This opens a list of items that modify the shelf. Using these options, you can organize shelf buttons in individual tabs, such as a Modeling tab, Animation tab, Lighting tab, and so on, to accommodate different workflows.