-더라 reports something the speaker witnessed for themselves; adding 고 하다 passes that report on second-hand, and in speech it nearly always contracts to -더래(요). So 바다에 나뭇가지가 하나 이렇게 떨어져 있더래요 is 'she said there was a branch lying there — she saw it'. The near neighbour -더라고요 is you reporting your own observation directly; -더래요 is you relaying someone else's.