It's called a double unary. It is used to convert an internal array of TRUE/FALSE into 1/0
This is a good source for further explanations.
http://xldynamic.com/source/xld.SUMPRODUCT.html
The Weekday part tests the weekday of the date which ends up giving you...
{3,4,5,6,0,1,2,3,4,5,6,0,1,2,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}<5)
Now when you check for less than 5 (Sat and Sun), the numbers turn into TRUE/FALSE which is multiplied by the first TRUE/FALSE looking for the word "SICK".
To get a better understanding of how and what a formula is doing, use the Evaluate Formula function