The active cursor shows the location at which editing commands will take effect, which is called point1. Many Emacs commands move point to different places in the buffer; for example, you can place point by clicking mouse button 1 (normally the left button) at the desired location.
While the cursor appears to be on a character, you should think of point as between two characters; it points before the character that appears under the cursor. For example, if your text looks like ‘frob’ with the cursor over the ‘b’, then point is between the ‘o’ and the ‘b’. If you insert the character ‘!’ at that position, the result is ‘fro!b’, with point between the ‘!’ and the ‘b’. Thus, the cursor remains over the ‘b’, as before.
Sometimes people speak of “the cursor” when they mean “point,” or speak of commands that move point as “cursor motion” commands.
If you are editing several files in Emacs, each in its own buffer, each buffer has its own point location. A buffer that is not currently displayed remembers its point location in case you display it again later. When Emacs displays multiple windows, each window has its own point location. If the same buffer appears in more than one window, each window has its own point position in that buffer.
On a graphical display, Emacs shows a cursor in each window; the selected window's cursor is solid and blinking, and the other cursors are hollow. On a text-only terminal, there is just one cursor, in the selected window; even though the unselected windows have their own point positions, they do not display a cursor. See Cursor Display, for customizable variables that control cursor display.
[1] The term “point” comes from the character ‘.’, which was the command in TECO (the language in which the original Emacs was written) for accessing the value now called “point.”