Mathematica uses a lot of syntactic sugar. You will find all Mathematica code unreadable until you've learned to read it; `//` is no exception.

I find Mathematica code unreadable full stop.

Its convenient when writing though.

I see Mathematica as a shell for math. You can write long programs or modules in it, sure, but very often you're simply typing up a couple of lines to check some computation or visualize an expression which you won't even save, in which case readability is secondary.

You're writing something and you decide you want to apply 'f' to it, so you type '// f' (instead of backspacing like a caveman). It's actually rather convenient.

Ah neat.

It's usually used with the formatting functions, so you have something like:

<Some big expression here> // Column

Useful where the function in question is an "afterthought".

That's just a matter of habit. The exact symbol isn't important anyway.