'Living Fossil' is a colloquial (rather then scientific) term applied to organisms which appear not to have changed in millions of years.

The term was coined by Charles Darwin in 1859 to describe Ornithorhynchus (the platypus) and Lepidosiren (the South American lungfish).

Modern-day evolutionary theorists point out that it's not possible to determine that an organism has not evolved at all - since DNA material is not available from ancient fossils.

Nonetheless, it's evident that many animals, plants, fungi etc etc have undergone very little change in their physical appearance - even over hundreds of millions of years. Example : Nautilus

The question arises - why has evolutionary pressure not changed an organism over such a long time? Are they, in a sense 'perfected' to such a degree that no 'improvements' can happen? Or has their evolution simply slowed down to an imperceptible rate - and if so, why?

[…] several hypotheses could explain morphological stasis on a geologically long time-scale. Early analyses of evolutionary rates emphasized the persistence of a taxon rather than rates of evolutionary change. Contemporary studies instead analyze rates and modes of phenotypic evolution, but most have focused on clades that are thought to be adaptive radiations rather than on those thought to be living fossils. Thus, very little is presently known about the evolutionary mechanisms that produce living fossils or how common they might be."

Source : Wikipedia

Wikipedia maintains a list of organisms routinely described as Living Fossils