Condensation is the phenomena in which a macroscopic number of bosons occupy the same microscopic quantum state. Usually, the number of bosons occupying a state with energy $E$ in a system held at a fixed temperature $T$ is given by the Bose-Einstein function
$$n(E) = \frac{1}{e^{E/T}-1}$$
However, another restriction is of course that all bosons in the system are at some state, therefore $\sum_E n(E) = N$ where $N$ is the total number of bosons. In the thermodynamic limit of large systems and continuous energy, the sum is replaced by an integral. This restriction introduces an energy shift to the system, if the number of bosons is conserved - the chemical potential $\mu(N,T)$, and the energies are calculated with respect to it.
As the temperature is lowered, more and more bosons shift to the low-energy states, but the general form of the Bose-Einstein function is respected. If the temperature, is lowered below a certain level, however, it might be that there are "too many" bosons to occupy the states, and so a large number of them condense into the state with the lowest energy.
In BCS superconductivity, the electrons (which are fermions) form Cooper pairs, and as each pair consist of two fermions, the pair itself is a boson. These pairs are then described by the Bose-Einstein statistic, and at low temperatures, depending on the geometry of the system, may condense such that almost all of them occupy the same quantum state.
