For keys that normally send a single character, Alt+key normally sends the escape character followed by this character. In particular, Alt+Backspace sends \e\177 where \e is the escape character (represented visually as ^[) and \177 is the backspace character (represented visually as ^? — more properly this is the delete character, but I'll use the name “backspace” in this answer). (Depending on your configuration, the backspace character may be \b instead, represented visually as ^H.)
When you press Ctrl+V Alt+Backspace, the Ctrl+V character tells the terminal (or the application, depending on the terminal mode) to interpret the next character literally, so this inserts an escape character, which is represented visually as ^[. Then the terminal has one more character to read, which is a backspace, which erases the escape character that you just entered.
To see the complete character string sent by a key, you can use this command, and type the key within 2 seconds:
stty raw; sleep 2; echo; stty cooked
stty raw switches the terminal to raw mode where control characters are just inserted as-is, and stty cooked switches it back. In practice Alt+Backspace is one of the very few cases where this is necessary though: most key chords only send either a single control character, or an escape character followed by printable characters.
In .inputrc, to cover both common cases (with the delete or backspace character):
"\e\177": backward-kill-word
"\e\b": backward-kill-word
Note that the escape sequence depends on your terminal. Some terminals don't send an escape sequence for some key chords, or send non-standard escape sequences, possibly the same for multiple key chords. But if you see ^[ briefly when you press Ctrl+V Alt+Backspace, it shows that your terminal does the standard thing for this particular key chord.
