One way to explain it is:
$A1 - The column A is absolute, which means it will not change no matter
where you should happen to copy the cell to from where the reference $A1
resides. However, the row will change according to how many rows plus or
minus you eventually paste the $A1 to. It will no longer be $A1 but $A & +
or - numRows.
A$1 - Same as above except that the row does not change and the column does.
$A$1 - This is an absolute reference which means that no matter where you
place it on the worksheet, it means cell A1 or cells(1, 1) or R1C1. The
first cell column A, Row 1.
I could go on, but there is abundant explanation in the help Excel help files.