The critical path is the sequence of activities that determines the minimum possible duration of the project. When viewed in a network diagram, the critical path is the longest path to the end of the project.

If the network diagram contains only Finish to Start relationships, any delay to an activity on the critical path will delay the completion date. If it contains other types of relationships (SS, FF, SF), this may not always be reflected in project management software. 

As an example, consider a network with 2 activities: activity A has a duration of 10 days and is predecessor with a Start to Start relationship to activity B, 20 days.  Most PM software will indicate that both activities are on the critical path, yet the software will allow A to be delayed up to 10 days without delaying project completion.

In fact, the above case is a misperception due to the software algorithm's shortcomings in identifying the critical path.  Only the very start (or first nanosecond) of A is on the critical path, as that is the only part of A which is a predecessor of B's start.  The true situation is that A's start is on the critical path -- if the start of A is delayed it will delay project completion.  However, the rest of A, including its finish, is not on the critical path, and in fact has ten days of total float -- it may be delayed up to 10 days without prolonging the project. 

However, almost all software algorithms are unable to make the distinction that an activity's start and finish may have different amounts of float, and therefore they show the entirety of A as being on the critical path.

Critical Path Rebuttal...

While the description of the two activities show critical path in the software is technically true, it is submitted that those activities are scheduled incorrectly in the first place.  That incorrect scheduling is the true root cause of the software "error".

The point of the two activities showing a SS-0 relationship is because we are actually saying those two activities can be worked in parallel.  We could further say that both of them in parallel would need to be done before a third activity.

To correct the schedule error, one would delete the SS-0 tie from the shorter, activity A, as a predecessor to the longer activity B.  You add a SS-0 tie from the activity B to the shorter activity A.  Then you make a FS-0 tie from each of them to a new third activity C.  When the project is scheduled we now see those same two activities in parallel with the same dates as before.  However, the shorter activity A shows 10 days of Total AND Free Float as what is expected to be seen.

Just because a user CAN make the software show a scheduling error does not mean it is a valid scheduling technique or methodology.  The error is a scheduling error and it should be repaired to show the proper relationship and float values.