Greetings,
A few things to help you understand this better.
Hibernate is not typically used on a desktop, sleep is more common.
Difference:
Sleep holds the computer's system state in memory and requires constant power.
Hibernate holds the computer's system state on the hard drive. In this case, its possible for the system to be completely powered off with no power consumption.
Note: there are trade off to the behavior and what is supported (see below)
There is no standard windows function that will put a computer into sleep or hibernation using the mouse. You can use it to select Sleep or Hibernation from the Start Menu.
During Hibernation, the system can be woken up using the power button, the mouse or keyboard will not wake the PC (unless) your power supply supports this. So in actuality power is still present, but your system state will not be lost in the event of a complete power failure.
Waking the system using mouse or keyboard. If all of your installed devices and their drivers support Sleep (also called S3 or low power state) the Sleep option should be present on your Start Menu under Power.
The second image are your power management settings. Control Panel > Power Options > Choose What The Power Buttons Do. Here you can check for the presence of Sleep and Hibernate options.
Important The mere presence of a button or enabling an option does not mean Sleep or Hibernate will work on your system. Again, this depends on installed devices and drivers for support.
BIOS - Please review Power Management settings in your manual Page 31
https://download.gigabyte.com/FileList/Manual/mb_manual_ga-h110m-s2h(gsm)(ddr3)_e.pdfPay particular attention to Power On By Keyboard and Power On By Mouse. Note, these features require a power supply that provides 1A on the +5VSB lead.
** Do not enable ErP (you can read why).
Experiment with the above settings / options and see if you can achieve the desired result. Make note of your changes so you can revert them should something not work as expected.
This should get you started.