Short tutorial on relative, mixed and absolute references in a spreadsheet. This is not really Calc specific.
When used in cell B2:
A1 refers to the cell one row above and one column to the left.
Copying down: A2, A3, A4, ...
Copying to the right: B1, C1, D1, ...
Copying up: A#REF! [A is valid but there is no further row above row above A1]
Copying to the left: #REF!1 [Row 1 is valid but there is no further column left of A1]
$A1 refers to the cell one row above in column A.
Copying down: $A2, $A3, $A4, ...
Copying to the right: remains $A1
A$1 refers to the cell in row #1 and one column to the left.
Copying down: remains A$1
Copying to the right: B$1, C$1, D$1, ...
$A$1 refers to the cell A1
Copying down: remains $A$1
Copying to the right: $A$1
Same with A1:B5, A1:$B5, A1:B$5,...
Rarely used and Calc specific: Sheet2.A1 vs. $Sheet2.A1 when copied across sheets.
The $ creates an absolute reference, so $B is always specifically column B.
Without that $, you have a relative reference, meaning a position relative to whatever the current position is, so it changes for each cell where the reference is placed.
In other words: The $ "freezes" the following row or column.
Moving (Cut&Paste) references rather than copy does not adjust relative references.
Tip: Shift+F4 toggles the active cell's references A1-->$A$1-->A$1-->$A1 and back to A1. This works also with selected portions of a formula while in edit mode.