I looked for a documentation section that concisely defined what the Front End is but I did not find one therefore I shall attempt my own definition. I admit I have never considered this in detail nor dug into the low level connection between the Front End and Kernel, so this definition is bound to be incomplete and possibly incorrect.
The Front End is the entire GUI (graphical user interface) to Mathematica. It is the implementation of the Notebook Interface. The alternative is a text-based (command line) interface.
The Front End is responsible for accepting input from keyboard, mouse, etc. Typed input is converted into Box representation(1)(2)(3) that can be passed to the Kernel. Menu commands, mouse clicks, etc., perform operations that may be applied by the Front End itself or which invoke Kernel evaluation, or a combination of both.
The Front End renders Box forms, directly input or passed back from the Kernel, in a human bearable way. These range from the simple
SubscriptBox types to all graphics and dynamic expressions. (One may use the menu command Cell > Show Expression to see the box structure of any Notebook cell.) Syntax highlighting, spacing and line breaks are applied by the Front End.
Some Front End rendering requires interaction with the Kernel. In recent versions even
FrameTicks may rely on Kernel evaluation so graphics may not display completely until a Kernel is started and definitions are loaded.
Dynamic expressions have their own evaluation channel to the Kernel in parallel to the normal evaluation channel employed by Shift+Enter.