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How well a solution to some problem will work when the size of the problem increases.
For example, a central server of some kind with ten clients may perform adequately but with a thousand clients it might fail to meet response time requirements. In this case, the average response time probably scales linearly with the number of clients, we say it has a complexity of O(N) ("order N") but there are problems with other complexities. E.g. if we want N nodes in a network to be able to communicate with each other, we could connect each one to a central exchange, requiring O(N) wires or we could provide a direct connection between each pair, requiring O(N^2) wires (the exact number or formula is not usually so important as the highest power of N involved).