The dollar sign is used as a set identifier here and is representing the records of the current selection.
Please check the Help, set analysis, for more details.
I also found this series of blogs quite useful:
By default, all selections will affect the results of the expression. You can specifically prevent selections from being applied to your expression. For example
will ignore selections on the Category field.
If by dimension, you are referring to chart dimensions, then the TOTAL clause will control which chart dimensions affect your expression. For exampe
Sum(TOTAL <Category> Value)
will ignore the Category dimension when calculating the sum (ie will tota all Category values without regard to the dimension)
Hope that helps