Dollar-sign expansions are definitions of text replacements used in the script or in expressions. This process is known as expansion - even if the new text is shorter. The replacement is made just before the script statement or the expression is evaluated. Technically it is a macro expansion.
The expansion always begins with '$(' and ends with ')'. For example: $(variablename). The content between brackets defines how the text replacement will be done.
For more information and examples, see:
Information note A dollar-sign expansion is limited in how many expansions it can calculate. Any expansion with over 1000 levels of nested expansions will not be calculated.