Machine Varnishing is a standard procedure for most printers. Varnishing is usually applied where bleed of a solid image bleeds off the page or where a large solid area is applied to the stock, basically where a printer would trim through a solid part of a finished job.
Varnishes basically enable the printed areas to be protected from the outside world with a clear ink base layer. This layer can be applied as a standard matt or gloss finish depending on the base stock or the desired affect. Varnishes are applied to most business cards or large printed areas. The main reason for varnishing is to prevent scuffing of the base ink, for example a solid on the back of a business would require a varnish to prevent the solid area from scuffing onto the card in front once being handled. Different stocks react differently and so may require more than one layer of varnish.
Keep mind to get the best result out of varnishes it is always best to let each layer dry 100% before a new layer is applied, some stocks will react badly with varnishes and will take even longer to dry if the base coat isn’t dry. 24hrs is a normal period for ink to dry and be rehandled. The varnish layer mind you will eventually rub off until the ink layer is exposed. The only way to prevent such problems occuring is to cellosheen / laminate the product. Varnishes can also affect a colours finish. If PMS / Pantone Reflex Blue is the base colour and varnish is applied over the top, the varnish removes/hides the red/reflex part out of the colour. The same goes for most colours. We find with black when it dries it turns a slight brown black, once a varnish is applied the black turns more a blue black which would be the prefered black.
Generally Matt varnish is for uncoated stocks, Gloss varnish is for coated stocks. Applying a gloss varnish to an uncoated stock once printed will normally highlight the fibres in a stock and so a solid can look a little more shinier.

Left side / majority matt varnished. Left print is unvarnished, Right is varnished.