Z-index controls which overlapping item appears in front of another. Imagine two sheets of paper on a desk: the sheet placed on top covers part of the one below.
A site might use this setting to place a pop-up above a page or keep a menu above a picture. A larger number often means “closer to the front” within the same layering context.
If a high z-index seems to have no effect, another group of elements may create its own layer. Use a small, consistent set of layer levels instead of giving every item an enormous number.