Acoelomates, Pseudocoelomates, and Coelomates:
Because it is triploblastic, a bilaterian has the capacity to form a
coelom. You may recall that a true coelom is a fluid-filled (occasionally, an air-filled) body cavity that is entirely lined by
mesodermal tissue. Obviously, only an organism that actually
has mesoderm can have a true coelom, so radiate animals cannot be coelomates. You may also recall that many internal organs are derived from mesodermal tissue, so triploblastic animals generally have much more complex bodies than do diploblastic animals.
We often divide the Bilateria into the
acoelomates, the
pseudocoelomates, and the
coelomates, according to what kind of coelom (if any) is present. These terms are simply descriptions of how animals’ bodies are built; they do not necessarily indicate evolutionary relationships.
An acoelomate is any triploblastic animal that has
no internal, fluid-filled body cavity. (“A” means “without,” so an “acoelomate” is “without a coelom.”) In an acoelomate, the space between the
ectoderm and the
endoderm is occupied by organs derived from mesodermal tissue, plus a loose collection of mesodermally-derived cells called
parenchyma.
You may recall that, since water is incompressible, a coelom, if present, can form a
hydrostatic skeleton that helps its possessor resist external pressure. A hydrostatic skeleton can also be used to help redirect force produced by muscle contractions. Because they lack internal skeletons of any sort, few acoelomates are capable of burrowing, since they cannot resist external pressure. Similarly, few acoelomates can generate sufficient muscle force to be capable of swimming.
Because they cannot resist external pressure, most acoelomates are pressed flat by a combination of the downward pull of gravity and the pressure exerted by the surrounding atmosphere or water. That’s why these animals are frequently referred to as “flatworms.”

A cross-section through the body of a typical acoelomate (in this case, a member
of the phylum Platyhelminthes). Note how there is no internal body cavity of any sort.
You can also see that the animal’s body is flattened by gravity and external pressure.