In a causality relationship a sufficient condition (or variable) is any variable which is sufficient to bring about the effect in question. A necessary condition is one that must be satisfied for the statement to be true. An example of sufficient condition is that a growing unemployment rate might be sufficient to cause an increase in the crime rate. Obviously many other factors (variables) could also cause the increase. Typically there are many conditions that are sufficient condition to cause an increase, or a decrease, in crime. To assert that one statement is a necessary and sufficient condition of another means that the former statement is true only if the latter is true. The concepts of necessary conditions and sufficient conditions help us understand and explain the different kinds of connections between concepts, and how different states of affairs are related to each other.
A condition A is said to be sufficient condition for a condition B, if, and only if, the truth/existence/occurrence, as the case may be, of A guarantees or brings about the truth/existence/occurrence of B.
For example, while air is a necessary condition for human life, it is by no means a sufficient condition, that is, it does not, by itself, alone suffice for human life. While someone may have air to breathe, that person will still die without water, has taken poison, is exposed to extremes of cold or heat, etc.
The foregoing is a complete set of necessary conditions, i.e. the set comprises a set of sufficient condition for x's being square. Frequently the terminology of "individually necessary" and "jointly sufficient" is used. One might say, for example, "each of the members of the foregoing set is individually necessary and, taken all together, they are jointly sufficient for x's being a square."