Why do we use the term "back up" when we are going in reverse? This is sometimes confusing for young English Language learners. Going backwards is understandable, where does the word "up" fit in? Are we moving in two directions?
Why do we say "back up" when we are going in reverse?
The word up has many definitions, but here it means to a source or origin. The word back here is acting as shorthand for backwards or drive in reverse. Thus putting the two together, we get the following statement:
Drive in reverse toward your point of origin
But that's a mouthful; saying, "Back up," is so much easier.
The word up can have literal spatial meaning with respect to a vertical or horizontal axis. To climb up a ladder. To walk up a ramp. To take the elevator or lift up to the 10th floor. We're going up to London (destination).
But it also has a more abstract figurative meaning, originating in the semantic realm of motion, specifically as it relates to the commencement or initiation of actions. The actor moves from a state of inaction, understood (at some deep metaphorical level) figuratively as a kind of recumbency, to a state of action.
He said, "I told you to back up, motherf_cker !" So I backed down and backed up.
P.S. Compare German auf, e.g. Hör auf ! (i.e. "desist!").
Of course, you are right, it is difficult to find the logic behind "up". My guess would be "to back" is derived from "to go back(wards)" and "up" is just an enforcing element as in to finish sth up.
As noted "back" in the phrase "back up" or "backing up" as used to describe going in reverse is easy to understand. For me the connection to up was made when I drove a 1960s era column shift vehicle. What is often referred to as a "three on the tree" to describe a three speed manual shift with shifter on the column. To place the car in reverse one had to pull the shift lever back and then push up. Thus "back and up" was the action taken to go in reverse. For me I equate "backing up" to the "back and up" shifter movement.
I can't say with any authority if that contributed to the term or if that shifter movement was some automotive engineers idea of a bad pun. Seems reasonable that in future times people may believe up in "backup" as applied to data storage comes from the concept of "the cloud" being up.
When it comes to verb-particle phrases, it is often not possible to give a generally applicable rule. It's just important to be aware that English as many of these, and learn them individually. Other "up" verb phrases where the "up" seems arbitrary include "shut up" (stop talking), "hook up", "look up" [a word in the dictionary], "catch up", "put up" (as in to put someone up at your house = to let someone stay at your house overnight), and "lock up".
Yall are focused on the words too much. It comes from the old manual transmissions that had "3 on the tree" or a manual shift lever on the steering column. To put the vehicle in reverse you had to pull the shifter back and up
This phrase doesn't actually make a lot of sense literally, especially pertaining to the word "up" in the sentence. This is because this is an inseparable phrasal verb, which means that the part with meaning (back) cannot be separated from the part that doesn't have meaning (up).
You can think about it this way in order to separate the lexical part:
To back something up
You can also understand this is through context:
I am backing up by 10 meters.
The opposite would simply be:
I am walking forward by 10 meters.
In both of these examples, movement is happening in only one direction.
If you are interested in a very helpful list of phrasal verbs including this one, you can find one here.
Also see Omnidisciplinarianist's answer for another great way to understand this.