In project schedule, you can have two different types of critical activities. Both of the type are made by different ways and have different purpose in project schedule management. 

Longest Path:

This critical path shows longest activity in your schedule. Or it could be a longest set of activities in your schedule. But you may ask, why the longest activity or set of activities are critical? The answer is simple. The longest activity or the longest set of activities consume most of your project time, they most probably need most of your budget and resources. Also, since these activity (ies) are the longest, these post more risk and cause more issues in the project. Moreover, you need more attention and effort on these activities.

Look at this critical activity (Longest Path) example: 

That's the reason, that longest activity(ies) are considered longest. But you might say, that is a good reason to call an activity or activities 'critical' but that isn't a significant reason perhaps to call an activity critical. Well, I would agree with you. And that is why we have another type of critical activities, which are described below:

Total Float = 0

These critical activities have no name like 'Longest Path' but these are formed when these have no margin left. In other words, these cannot be delayed further. And if they do delay, they will delay the project. Look at the Total Float=0 critical activities example below:

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