The Option/Alt symbol (⌥) is probably one of the most-used symbols for shortcuts on a mac (outside of Command), but it was left off the keyboard for some reason.
The Command Key Symbol's Origin Story is very interesting with a comment from Steve Jobs and a look into how the team found inspiration for a new symbol (to replace the open apple icon). Unfortunately there isn't a similar story for the symbol for Option/Alt. The best we have is internet conjecture.
The general consensus is that the symbol is that of a switch. Switches are used very commonly within computers. I don't just mean switches like the power button on your computer, but also inside the processor and other computer chips there are tons of switches. When a switch is drawn on an electrical diagram, it looks like this:
Although switches in a computer are similar, they're still not quite right. The lines don't quite match. Here's the symbol for easy comparison:
You can see on the Mac symbol, that the line on the left is top-aligned. It might just be a stylistic difference, but it also could represent something a little more common (outside of the geek world).
To some, the symbol looks like the train on a track. The train starts from the left and can continue straight, on the main path. Or you could throw the switch and go down on the lower track; the alternate track if you will. You have the option of choosing which path you'd like to take.
Memorizing the Option Alt symbol
The option/alt symbol is typically used as a way of getting an optional, or alternate letter on your keyboard. For example, open a text editor and press the "A" key on the keyboard. You should see a lowercase 'a' show up.
Now, press the "A" key again, but make sure you're holding down the Option/Alt key before, during, and after pressing "A". (You can let go now). You'll likely see a lowercase 'a' that looks a little different: å.
In the normal, main path, you get an 'a'. Or you have the option of getting an alternative 'å'.
So when you see a symbol in the menu, that looks like you can choose to take one of two paths, it's telling you to use the option/alt key to choose the optional or alternative road.
Go try it out by holding the option/alt key and pressing the speaker icon on the top of your screen. You'll see an alternative menu to the one you'd normally see.