Plain English Meaning
When you're flying IFR but the weather near the airport is good enough that you can see where you're going, you can ask ATC for permission to fly visually to the airport instead of flying the full instrument approach. ATC has to approve it, and you have to be the one who asks.
Full Definition
An approach procedure that may be used by a pilot operating on an IFR flight plan, in lieu of conducting a published instrument approach, when the pilot is clear of clouds, has at least one statute mile flight visibility, can reasonably expect to continue to the destination airport in those conditions, and specifically requests it from ATC. The destination airport must have a published instrument approach procedure, and ATC must approve the request.