An array is basically a list of variables. In his code above, he created it with "VAR ARRAY[5]" meaning its a list of 5 variables. You can access any one by writing ARRAY[n]. To set one you might say ARRAY[3] = 2. This would set variable at index 3 to a value of 2. Keep in mind that the indices start at 0 though. So n can be any number in the range of 0-4 in this case to access your 5 variables.
If you want to save data for the next time the program is run, you will have to use the SAVE command like TheV360 showed to write that data into a file so you can load it the next time the program is run (using the LOAD command). You can check if the save file exists before loading it too by using the CHKFILE command.