Definition?

Yup - "on the lees" generally refers to some extended time aging with lees still in the aging vessel.

With grape wines, fruit wines and melomels where the fruit is added in primary, the first lees to drop will include bits of fruit, etc., that you really don't want to leave in very long, since when that stuff begins to break down it can lead to some off flavors, or can support the growth of spoilage organisms. That stuff is usually called the "gross lees." Sur lie aging, or aging on the lees, usually refers to aging on the "fine lees," which are the dead/dormant yeast cells that fall out of suspension when fermentation activity slows. Settling of the fine lees generally doesn't happen until you've racked into a secondary or aging vessel.

It will add something, and whether it is good or bad depends on your preference, the management of the lees, and the type of yeast. Typical desirable flavors that come from extended lees exposure are things like bready, toasty, yeasty, and creamy. Be sure to use a yeast strain noted for it's lees aging potential; some strains like 71B are known for producing rather unpleasant flavors. D47 on the other hand is known for a tropical fruit character that comes with lees exposure (pretty unique!).

If you can find one, get a bottle of 'late disgorged' sparkling wine and try it side-by-side with another bottle of "regular" sparkling from the same year. [sparklers of the Methode Champenoise persuasion are separated from the yeast used to make them bubbly by "disgorging". 'late disgorged' just means the bottles spent extra time--sometimes a year or two more--with the yeast in the bottle.] The influence of the extra yeast exposure should be pretty apparent. And you get to drink bubbly in the name of science.

Actually some of those late disgorged bottles are done after decades (some pricey stuff that I've not tried), but even regular Champagne is notable for the bready/yeasty/toasty character of lees aging. To get a good comparison you might be better taking a true Champagne (from France - and it doesn't have to be expensive) and comparing with a dry sparkling wine that isn't lees ages such as a Prosecco from Italy. The difference the yeast makes should be very apparent between the two.

Very true, you can tell I'm spoiled on the California sparklers. Out here many are disgorged fairly early to produce bright, lemony bubbly and it's not until you get to the "fancy" ones where the classic French Champagne character comes out.