It's used to describe something that is done with ease and smoothness, similar to how a knife glides through butter.
Here are some examples:
* "The job interview went like a knife through butter; I felt confident and answered all the questions easily."
* "The negotiations went like a knife through butter, and we reached an agreement quickly."
While "on velvet" isn't a common idiom, it might be used figuratively to describe something that is smooth, comfortable, or luxurious.