More than likely it is a heater outlet hose, but the gunk around it - if that is from the leak, appears to be oil - so likely it is from the valve cover - if you have a V6 - both sides should be replaced. The Hose is old and shows blistering (swelling) so it too will have to be swapped out for a new one.
As far as parts go - this should be a 5/8" to 3/4" (1" max) diameter hose.