From ??Paul Bradshaw <pbradshaw@advsol.com>??:

A "hungry delete" swallows up all whitespace when pressed, rather than just one space, tab, or line-feed at a time.

For instance, when you have this (where "|" is the caret):

public foo()
{
        // some code
        *|*
}

Pressing ??delete?? will get you to this:

public foo()
{
        // some code
*|*
}

But pressing a ??hungry delete?? will get you to this:

public foo()
{
        // some code|
}

Which is much more logical, as it's the exact inverse of pressing enter (i.e., pressing enter auto-indents and opens a new line... pressing hungry delete deletes the indent and closes the line).