When people write 'with' they sometimes write w/. Why do they do that?

It is a form of shorthand... the slash indicates that what follows is "with" what preceeded...

It's a heck of a lot easier to write that than to spell out all the words... and since it is relatively commonly understood, there's usually no problem with using it.

When I take notes at church, I often use "J.C." and "H.S." to refer to Jesus and the Holy Spirit, respectively... "w/" is just another example of a shortened version of "with"

I'm amused to note that with the widespread advent of Internet Messaging... that abbreviations and emoticons are proliferating... LOL!

Also, w/o is often used to abbreviate 'without'