This question is not asking for a list (as in Shiv'a - mi yodeya?) but rather what is the basic significance to the number 7 that would cause it to be chosen for so many things. Ramban (Nachmanides) says that this is based on the 6+1 (7) days of creation which includes Shabbat. That is, 7 shows the completion of the physical universe and of nature. That is also why the bris (as one example) is on the eighth day as showing that one is going above and beyond the physical universe.
I have seen references to the seven physical dimensions that define the universe, six of space and one of time.
7. time - connects the other six and allows movement or change (ruach)
Note that within the universe time only goes in one direction. Once something has happened we cannot travel back as we can with the spacial elements. Memory is what allows a human being to connect to the past, but "times arrow" flies in one "direction" only. As I said, the seventh element is shown by Shabbat which completes the universe and allows all the previous (physical) elements to continue to exist.
Some use ruach of neshama as the seventh connecting element. They also use the Maharal's concept that the six are the elements of space (physicality) and that the seventh (symbolised by Shabbat) is the central (spiritual) element that connects them all and allows them to interact. One can see that given a solid shape, such as a cube or a sphere, one can put only six of those objects around it (of the same size) and still allow them all to touch the center and be connected.
Each of the items that use the number seven within Judaism continues from this consideration to show connection to creation and would have a separate analysis extending from this basic concept.