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Let $\Omega$ be the sample space for an experiment, and, $F$ is the power set of $\Omega$.

If the experiment consists of just one flip of a fair coin, then the outcome is either heads or tails: $\Omega=\{H,T\}$, then $F=\{\emptyset,\{H\},\{T\},\{H, T\}\}$

Why is a null set included in the power set of sample space? What is its significance with regards to this experiment?

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    Because the power set $\mathcal P(A)$ of **every** set $A$ must include **all** subsets of the original set $A$, and the emptyset is a subset of every set : $\emptyset \subseteq A$, for every $A$. – 2017-01-06
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    @MauroALLEGRANZA That is true, however, an event is defined as the set of outcomes of an experiment. Doesn't the inclusion of null set in the set of events imply that the experiment is not being conducted? What I mean to ask is, are there cases where a null set is a likely outcome of an experiment? – 2017-01-06
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    @Zwolf The null set always always always has probability $0$. – 2017-01-06

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Well first of all, the power set includes ALL subsets. The empty set is a subset and thus it is included.

However I don't think this is what you are asking. In the $\sigma$ algebra, why should one include the empty set? Well the $\sigma$ algebra are the sets you know the probability of. The empty set is the event that nothing happens. If you flip a coin, what is the probability that nothing happens? You don't get a head, or a tail, you get nothing. Well obviously the probability is $0$. So you know the probability of this happening, so it should be included in a $\sigma$ algebra.

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    I have no issue with your answer, but check the comment the OP just posted. Would it be fair to say that it is a necessity in the construction of the sigma algebra to guarantee closure under complementation? – 2017-01-06
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    @AntoniParellada I think complementation is a separate issue. If you know the probability of something happening, you know the probability of it NOT happening (which is the complement). – 2017-01-06
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The meaning of $\{H\}\cup\{T\}=\{H,T\}$ is the clear statement: "Head or Tail".

The same way $\{H\}\cap\{T\}=\emptyset$ means that "Head and Tail" which is impossible.

So, $\emptyset$ is a meaningful member of $F$.