Varnish is a protector. Since oil paintings are not usually displayed under glass like watercolor, gouache, or other works on paper, they can collect dust and grime from the air which, over time, will make them appear dark and dirty. Varnish can be removed and then reapplied. The paint underneath the varnish will still be fresh looking after the varnish is removed, but removing and reapplying varnish can be tricky business. It is important not to damage the painting underneath. From a collector's standpoint, varnish is a good idea because it will protect the painting from all the crud that floats around in the air. If I were spending a lot of money on an oil painting with an eye toward investment or toward preserving family history, I would definitely want it varnished. If I were buying a painting to decorate my kitchen, it might not matter.
This one looks like a wonderful family portrait that probably should be varnished.