The Collaborative International Dictionary
Lamellibranchia \La*mel`li*bran"chi*a\, Lamellibranchiata \La*mel`li*bran`chi*a"ta\, n. pl. [NL. See lamella, and Branchia, Branchiate.] (Zo["o]l.) An earlier name for the class of Mollusca including all those that have bivalve shells, as the clams, oysters, mussels, etc., now called Pelecypoda or Bivalvia.
Note: They usually have two (rarely but one) flat, lamelliform gills on each side of the body. They have an imperfectly developed head, concealed within the shell, whence they are called {Acephala}. Called also Conchifera, and Pelecypoda. See Bivalve.
Conchifera \Con*chif"e*ra\, n. pl. [NL., fr. L. concha + ferre to bear.] (Zo["o]l.) That class of Mollusca which includes the bivalve shells; the Lamellibranchiata. See Mollusca.
Wikipedia
Conchifera is a subphylum of the phylum Mollusca. It comprises all of the shell-bearing classes of molluscs, including the snails, clams, tusk shells, ammonites, monoplacophorans, and so on. The other one is Aculifera.
This taxonomic term is used mostly by paleontologists, and not by scientists who study the living molluscs.