Rooting is the process of allowing the device user to gain privileged control also know as Root access. After root you can eliminate some software and hardware limitations put by the manufacturer.
Rooting is also compared to jailbreaking which is done in IOS devices.
In simple words in Samsung and Xiaomi there are some pre-installed apps which are of no use to some users so after Root you can be able to remove those apps.
Also for some advance user Root can help some software to run on Android which can perform Hardware tweaks such as Overclocking and Under clocking cpu which helps to boot device performance and battery backup.