It is in fact based on the font you're using, and how it's built, as @Alex mentioned above. Here's an example of four different fonts, same font size, exact same setting in each text box:
The first font is standard Arial. The second it a fairly common sans-serif font, AG Book Pro. The third and fourth are fancier fonts I got from dafont.com. As you can see, the more standard fonts have very little to no spacing around them at all. The other two have random spacing either at the top or bottom.
As a side note, it's also possible to change the spacing around text by using the Text Frame Options dialog (Cmd+B on Mac, Ctrl+B on PC), and editing the "Inset Spacing" numbers. You can do it uniformly by keeping the "link" icon clicked, or unclick it to edit the dimensions individually for top-left-bottom-right.
I don't think this is the cause of OP's issue, however.