The Latin letter is used in mathematics to represent the name of a generic math function. Typically, the symbol is used in an expression like this:
In plain language, this expression represents the function named that takes in the variable as input.
The capital Latin letter F is used in mathematics to represent the antiderivative of a function.
A function takes input and produces output. The idea is a useful way to abstract away complexity and, especially in the age of computers, is a practical tool to solve problems.