Complex is the opposite of simple. Think of something that is made up of many (moving) parts and you have complex.
Wiki describes complexity as the behaviour of a system or model whose components interact in multiple ways and follow local rules It characterizes something with many parts where those parts interact with each other in multiple ways, culminating in a higher order of emergence greater than the sum of its parts. Science takes a number of approaches to characterize complexity. A group or system of different things that are linked in a close or complicated way; a network.
Complexity might be described as something that cannot emerge without intelligence. elaborated.