Word Echoing is when you repeat the same word or phrase in your writing. It's even more obvious when written within one sentence.
For example, 'We met Sam and Ian before we met Dan.' 'Met' here is echoed - obviously, this is a gratuitous example but you get the idea.
Stylistic Echoes can also enter our writing, starting sentences with prepositional phrases for example; after showing his badge, when he knelt down, as they drove home.
'As they walked, David noticed many cubicle doors were open which allowed a sneak peek into the offices.'
This could be re-written as.
'Many of the cubicle doors were open allowing a sneak peek into the offices.'