A class of particles which have a half- integer spin are called fermions. Example - proton, neutron, electron, etc. Unlike bosons, only two fermions (at maximum) can go to the same quantum state, as dictated by the Pauli Exclusion Principle. They obey Fermi-Dirac statistics. The wave function associated with fermions is anti-symmetric.
An atom can also be classified as a composite boson or a composite fermion. To find whether an atom is a composite boson or a composite fermion, you need to look at the net spin of the atom due to its constituent particles that make it. For example, consider the simplest of the atoms - Hydrogen. Hydrogen has a proton and an electron. A proton is a half-integer particle and so is an electron. Therefore, the net spin of a normal hydrogen atom is one, which is an integer. Therefore, hydrogen is a composite boson. If we consider a helium-4 atom, there are two protons, two neutrons and two electrons. Each of these particles has a half integer spin. Therefore, the net spin of a normal helium atom is an integer. Hence, helium is a composite boson. What's about lithium-7 ? A lithium-7 atom has three protons, four neutrons and three electrons. Therefore, the net spin of a lithium-7 atom is an integer and hence it is a composite boson. On the other hand, by the same way of reasoning, lithium-6 is a composite fermion.
In general, an atom can be classified as a composite boson or a composite fermion on the basis of the total number of constituent particles contained in it. If the total number of constituent particles is even it is a composite boson where as if the total number of constituent particles is odd, it is a composite fermion !