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.