Free Slack is the number of days that an activity can have before it starts delaying the next (successor) activity.
Total Slack is the number of days that activity can have before it starts delaying the whole project.
Let's assume that we have a project that consists of 4 tasks:
Task A: Starts on July 4th and Ends on July 5th (July 4th is a holiday, so that must be a bad project manager who planned this schedule!)
Task B: Starts on July 8th and Ends on July 8th
Task C: Starts on July 11th and Ends on July 11th
Task D: Starts on July 14th and Ends on July 15th
So, the whole project ends on July 15th.
Task A has a free slack of 2 days (So, Task A has 2 more extra days before its starts delaying the next activity - the free slack is the start date of the successor activity - the end date of the predecessor activity - 1)
Task B has a free slack of 0 days
Task C has a free slack of 2 days
Task D has a free slack of 0 days (obviously, because it's the last task)
Now let's calculate the total slack for each:
Task A has a total slack of 4 days
Task B has a total slack of 2 days
Task C has a total slack of 2 days
Task D has a total slack of 0 days
So how did we calculate the total slack of an activity? In short the total slack of an activity is its current free slack + the free slack of the remaining activities. Here's the formula:
TS(A) = FS(A) + Σ(FS(remaining tasks))
(Note: TS = Total Slack, FS = Free Slack)
Now anyone can easily understand the point behind free slack (we need to know if a task is delayed, how much time can it be delayed without affecting its successor), but why do we need to know what the total slack is? Let's assume that a task is taking much more longer than expected; it already exhausted its free slack. Assuming all the remaining tasks on the project will take the same duration, how much can this task drag on before delaying the whole project?
When the total slack is exhausted by one activity, it means that none of the remaining activities can take more than its original duration, or else, the whole project will be delayed.