Echoing broadly refers to the repetition of sounds. Imagine standing overlooking a canyon and yelling and your yell amplifies and repeats throughout the canyon - this is an echo.
In verbal speech, echoing this frequently occurs in individuals with autism spectrum disorders, Tourette Syndrome, schizophrenia, aphasia, and dementia. Called echolalia, the individual repeats words and phrases heard from another person and can be immediate or delayed.
An example of echolalia would be asking a person "Do you want to go for a ride?" - an echolalic response to this question would be "Do you want to go for a ride? Go for a ride? Do you want to go for a ride?" Instead of answering the question they are just echoing it.