Inhale is King Dedede's neutral B attack. Not to be confused with Kirby's inhale, where in he gains abilities from others, info from Whobby 08 indicates that Dedede simply spits his victims out.
Actual gameplay footage shows that King Dedede can walk around with his victims in himself, and can perform "Dededecide" (or "Regicide")
Much like Wario's Chomp, Dedede is able to swallow items using this attack.