Direct speech is used to give the exact words used by another speaker. The words are given between quotation marks (" ") in writing:
EG: "I'm coming now," he said.
Indirect Speech (also called Reported Speech) is used to communicate what someone else said, but without using the exact words. The tenses of the verbs are often changed.
EG: He said that he was going to come. (The person's exact words were "I'm going to come.")
For more, see this page.