Sur lie -  is the French expression or term for 'on the lees'. Lees are the coarse sediment, which consists mainly of dead yeast cells and small grape particles that accumulate at the bottom of vats or tanks during the fermentation process. Winemakers believe that certain wines benefit from being aged 'sur lie'. Chardonnay wines are a good candidate where the winemaker might look to add complexity - by ageing for a few months. The lees will be stirred (batonnage in French) in order to promote the uptake of the lees character into the wine.
This happens as a matter of course with Sparkling Wines made via Méthode Traditionnnelle because the second fermentation occurs inside the bottle where the wine is aged (sometimes for up to 10 years) until the lees are disgorged.

 

Muscat wines from the Loire wine region in France - occasionally have the phrase 'mis en bouteille sur lie' on the label. Which means the wine was bottled from barrels where the lees were not drained (although the sediment has fallen to the bottom of the barrel).
When yeast cells die, their cell walls breakdown, gradually releasing compounds into the wine as (e.g. glucose, amino acids, fatty acids, and manno-proteins). The compounds released can influence the structural integration of the wine in terms of; tannins, body, aroma, oxidative buffering and wine stability.

The primary reason for sur lie ageing are usually based on stylistic characters desired by the winemaker: to enhance the structure and mouth feel of a wine, giving the wine extra body and increase the aromatic complexity, depth of flavour, palate enagagement and length. Lees also absorb oxygen, assisting in maintaining a slow and controlled oxidation during maturation. Lees stirring can increase the release of yeast compounds into the wine. Stirring can result in a creamy, viscous mouth feel, and can enhance layers of flavour and complexity.
The lees are also an important component in the making of 'Ripasso' wine where the left-over lees from 'Amarone' are used to impart more flavour, complexity and colour to the partially aged Valpolicello wine.