What does the line #!/bin/sh mean in a UNIX shell script?

It's called a shebang, and tells the parent shell which interpreter should be used to execute the script.

e.g.

#!/usr/bin/perl   <--perl script'

#!/usr/bin/php <-- php script

#!/bin/false <--- do-nothing script, because false returns immediately anyways.

It's implemented as a comment so that anything coming in that line will not "relevant" to the interpreter specified. E.g. all scripting languages tend to understand that a line starting with # is a comment, and will ignore the !/usr/bin/whatever portion, which might otherwise be a syntax error in that particular language.

#! corresponds to the magic number 0x2321 (look it up in an ascii table). When the system sees that the magic number, it knows that it is dealing with a text script and reads until the next \n(there is a limit, but it escapes me atm).