Had to look over what we have done so far.
Serial
LCD
Some program flow.
Input from a switch

How about remembering something?
Let's say you have some parts moving along a conveyor and you want to count how many parts have passed by a certain point. But the problem is when the machine is turned off and then turned back on the counting starts back at zero and you want total parts counted for a week.

You can use the push button to simulate when a part passes by and have a WORD size variable increment each time the switch is activated and that value displayed someplace (serial or LCD).

To save the value for when the machine is turned off and on you will need to save the value to EEPROM and read from the EEPROM when the machine is started again. Place that value into the counting variable to continue counting from where it left off.

Another problem that can be addressed later is the EEPROM only has 1,000,000 write cycles so if the EEPROM is written to each time a part passes depending on how fast things are moving you could wear out the EEPROM in a matter of weeks.
So a shut down sequence is needed to only write to the EEPROM at shut down. This is not hard for scheduled shut downs but can be a "trick" for power failures.

For now you can have the value written to The EEPROM each time the variable is incremented.

Are you still using a 16F684 ?