It simply makes sure all the data was written correctly to the DVD. A write error could render the disc unplayable. And it takes a long time because it reads every bit of data written to the disc - all 4.7 or 8.5GB of it (single layer or dual layer disc).
You can skip the verification and nothing bad will happen to your computer, but an error on the disc would go undetected, until of course the worst possible moment. That being said, I've never had a disc written with errors... but is is possible, especially if you burn DVDs at the highest speed possible with your machine, or if you burn, say, an 8x disc at 16x speed.