The question is answered, but there is some more info missing:
Variable vs. Cmdlet
You have a value in $Date variable and -f operator does work in this form: 'format string' -f values. If you call Get-Date -format "yyyyMMdd" you call a command let with some parameters. The value "yyyyMMdd" is value for parameter Format (try help Get-Date -param Format).
-f operator
There is plenty of format strings, look at least at part1 and part2. She uses string.Format('format string', values'). Think of it as 'format-string' -f values, because -f operator works very similarly as string.Format method (although there are some differences (for more info look at question at StackOverflow: how exactly does the RHS of the -f operator work?