What is a module?

A module is a way to store variables and functions/subroutines that are available everywhere in the program and modifiable from anywhere in the program.

How to write a module

To store variables that must be accessible everywhere in a program, you need to create a file called (for example) mymodule.f90 which contains the following
module mymodule
implicit none
real :: a
real :: b
a = 5
b = 6
function functionInModule(x,y)
implicit none
real :: x, y, functionInModule
functionInModule = x-y
end function
end module
And the main program becomes
program myprogram
use mymodule
implicit none
real :: w, z
some code here
w = 2
z = functionInModule(w,w)
end program
Note the use mymodule at the beginning of the program before the implicit none. Because of this line, all the variables and functions/subroutines declared in the module can be used in the program.
One can also use use mymodule, only: variable/function/subroutine to make only part of the variables or functions available. For example
program myprogram
use mymodule, only: functionInModule
implicit none
real :: w,z,r
w = 1
r = 2
z = functionInModule(w,r)
end program
This can be done to make sure that other parameters contained in the module are not inadvertently modified in the program.