Origin of term ‘confluency’ in cell culture
Besides the etymologic explanation that @aandreev gave, in cell culture this term is commonly used to describe the density of adherent cells and it is used as a measure of their proliferation. It is usually combined with an estimated (or counted) percentage, so 10% confluency means that 10% of the surface the dish or flask used is covered with cells, 100% means that it is entirely covered. The cells grow twodimensional on the surface of the flask in this case. The picture below (from here) illustrates different levels of confluency:



The level of confluency is important as the cells change their growth with changing densities. Low density cells (10-20%) usually grow slower than 50% confluent cells. If the plate is complete grown by cells, they tend to grow much slower again. This influences their genetic program, behaviour in experiments and transfections.

As @Roland pointed out it is important to say that confluency is not a hard measure, but rather an estimate of the cell density. Different people will get different estimations, but the trend should be the same.