Hotkeys allow you to perform an action ingame with the keyboard that may otherwise require use of the mouse, allowing for more efficient play. Saving seconds here and there might not matter to a beginner but, if used, hotkeys can provide players with the much needed advantage of speed and accuracy on the battlefield.
Various hotkeys also offer powerful and specific tools to have your units follow your command with less effort.
For instance, you can start to save time right at the beginning of a battle. When your first barracks is ready to place and you hear EVA announce "construction complete", instead of manually clicking the icon on the sidebar you can simply press the Structures Tab (Default: Q) button which will bring up the structure for placement instantly. Now imagine the time saved across an entire match. Rather than going over to the sidebar with your mouse, taking your attention away from unit control just to place a structure, you can simply use the sidebar tab hotkeys to instantly place down finished buildings. That can make a big difference in a competitive match!
If you wish to alter the keyboard layout of these hotkeys go to Settings -> Game -> Configure Keys in the client menu to reorganise them in whatever way is most comfortable.
Control Groups are unit selections saved and recalled through hotkeys. This is useful for having a key units in your army immediately selectable without having to manually do it, for example to call in your aircraft without jumping back to base first.