An Excel formula is a way of defining a specific calculation in a worksheet. In Excel, all formulas must begin with an equals sign (=). For example, to add 100 to a value in A1, you can write a formula like this:
=A1+100
This formula will always add 100 to the value in A1, even when that value changes.
Formulas with Functions
Excel contains hundreds of pre-built formulas called functions. You can use functions on their own in formulas, or even combine multiple functions in a single formula.
For example, the this formula uses only the MAX function to calculate the maximum value in the first 100 cells in column A:
=MAX(A1:A100)
This formula uses the WORKDAY function to return a date 5 working days from a date in A1:
=WORKDAY(A1,5)
In a more complex example, this formula uses two functions to count the letter "a" in A1:
LEN(A1)-LEN(SUBSTITUTE(A1,"a",""))
See this page for a full explanation of this formula.
Formulas vs. Functions
All functions are formulas. However, you can create formulas in Excel without any functions at all. For example, this formula adds A1 to A2 without any functions:
=A1+A2