If you're not reflecting back, then you are assuming the majority of what someone says and stand a good chance of getting it wrong, especially if what is said is emotional, detailed or complicated. Many relationships and business deals inexplicably fall apart simply because of assumption piled upon assumption, until there is no way back to what was originally said.
One of the least used skills of listening is that of reflecting back, actually repeating back to the speaker in a neutral tone what we understand them to be saying. We tend not to do this because it feels a little awkward, possibly insulting. Also, many people who do reflect back use the old therapy language of "What I hear you saying is..." which has become a bit of an irritating cliche.
Just as in learning any new skill, at first one feels awkward and does things in a rote manner. But once one has it down, saying after an important piece of information is delivered "So, you're saying that..." or simply "You want/think...." An overt statement of "Let me make sure I have what you are saying right because I don't want to assume..." works for most heated or business situations.
When we do this, the speaker is usually complimented, affirmed and, if emotional, relieved. When we reflect back, we hold up what I call "The Mirrored Bowl;" we hold their story for them and hold it up so they can see it. Not only to we make sure we got it right, but they get to see themselves and what they have said, as well, allowing for correction, or sometimes, tears of relief from having been truly heard.