Ok, this isn't that tricky if you disect the command line switches one at a time:

This means essentially "execute the following code". As you can see, in this particular case, the following code is nothing at all; zilch.

This means wrap the -e code in the following loop:

while( <> ) {
    # -e code goes here (nothing, in this case)
    print $_;
}
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Now for the -i: That means do an in-place edit. Whatever characters immediately follow -i will be appended to the input file's name for the purpose of creating a backup file. Often you'll see -i.bak which means take file foo and create a backup named foo.bak. Well, in your case, instead of .bak you're using ~, so it creates a backup named foo~.

Now put it all together:

1. -i~ Do an in-place edit, but first create a backup file named "inputfile~" (or in your case, foo~).
2. -p loop over the input file (foo), and after executing the -e code, print the line to the output file (which is the same filename as the original input file, because you're doing in-place editing thanks to -i
3. -e Execute the following code within the while loop: '' (in other words, do nothing inside the loop except the -p loop's default; print.

I hope this helps, but if it doesn't, see perlrun for more detail. Also (shameless plug), I wrote a node awhile back that went into greater detail on the subject of learning how to compose Perl one liners. The node is here: Re: One Liners. I think you'll find it to be a pretty easy introduction to Perl's command line switches and Perl one-liners. Good luck!