Seven is measurably the most popular number in the world. Surveys asking people to name a favourite return seven more often than any other, typically by a wide margin, across countries and languages. That is a fact about people rather than about mathematics, and it has been studied.
Part of the explanation is arithmetical. Among the digits one to ten, seven is the only one that is neither a factor nor a multiple of any other in that range: two, four, six, eight and ten are all connected by doubling, three, six and nine by tripling, five and ten by fives. Seven sits alone. When people are asked to produce a random number between one and ten they choose seven far more often than chance allows, and the psychologists Michael Kubovy and Joseph Psotka showed in 1976 that the preference tracks exactly this quality of seeming least determined.
The other frequently cited result is George Miller's paper of 1956 on the magical number seven, plus or minus two, describing the limit on how many items can be held in immediate memory. It is one of the most cited papers in psychology and it is routinely misapplied. Miller himself opened by joking about being persecuted by an integer, and the capacity he described has since been revised downward, the working figure in current research is nearer four. The paper is evidence that seven is a memorable number, not that the mind is built on it.
None of this explains the ancient sevens, which came from the planets and the moon. It does explain why seven keeps being chosen now, in contexts with no astronomical content at all: seven wonders, seven seas, seven-league boots, and the seven that people reach for when asked to pick a number and mean nothing by it.