Reubo That 'hose' sits right below the condenser for the air conditioning. When the AC condenser gets cold, it will shed condensate (water) from its fins and that is meant to drain out that tube, the other end of which appears in the engine bay.
If you're getting water leaks there, you may need to look at the condition of the seal on that drain between the inside and outside of the firewall. It's not easy to find the outlet on the engine bay side, since it's directly below the inlet and outlet pipes for the condenser, etc.