In a regular expression, you can "capture" parts of the matched string with (brackets); in this case, you are capturing the (^|_) and ([a-z]) parts of the match. These are numbered starting at 1, so you have back-references 1 and 2. Match 0 is the whole matched string.
The /e modifier takes a replacement string, and substitutes backslash followed by a number (e.g. \1) with the appropriate back-reference - but because you're inside a string, you need to escape the backslash, so you get '\\1'. It then (effectively) runs eval to run the resulting string as though it was PHP code (which is why it's being deprecated, because it's easy to use eval in an insecure way).
The preg_replace_callback function instead takes a callback function and passes it an array containing the matched back-references. So where you would have written '\\1', you instead access element 1 of that parameter - e.g. if you have an anonymous function of the form function($matches) { ... }, the first back-reference is $matches[1] inside that function.
So a /e argument of
'do_stuff(\\1) . "and" . do_stuff(\\2)'
could become a callback of
function($m) { return do_stuff($m[1]) . "and" . do_stuff($m[2]); }
Or in your case
'strtoupper("\\2")'
could become
function($m) { return strtoupper($m[2]); }
Note that $m and $matches are not magic names, they're just the parameter name I gave when declaring my callback functions. Also, you don't have to pass an anonymous function, it could be a function name as a string, or something of the form array($object, $method), as with any callback in PHP, e.g.
function stuffy_callback($things) {
return do_stuff($things[1]) . "and" . do_stuff($things[2]);
}
$foo = preg_replace_callback('/([a-z]+) and ([a-z]+)/', 'stuffy_callback', 'fish and chips');
As with any function, you can't access variables outside your callback (from the surrounding scope) by default. When using an anonymous function, you can use the use keyword to import the variables you need to access, as discussed in the PHP manual. e.g. if the old argument was
'do_stuff(\\1, $foo)'
then the new callback might look like
function($m) use ($foo) { return do_stuff($m[1], $foo); }
preg_replace_callback is instead of the /e modifier on the regex, so you need to remove that flag from your "pattern" argument. So a pattern like /blah(.*)blah/mei would become /blah(.*)blah/mi./e modifier used a variant of addslashes() internally on the arguments, so some replacements used stripslashes() to remove it; in most cases, you probably want to remove the call to stripslashes from your new callback.