What is a hyper property?
A trace is a (finite or infinite) sequence of program steps. (Some works only consider finite traces, or only infinite ones.)

A property is a set of traces. E.g. all those traces where variable $x$ is never negative.

A hyperproperty is a set of sets of traces. E.g. the sets of traces $T$ where each trace in $T$ is finite.

Some complex security goals can not be described as a property. Non-interference, for instance, can not be checked on a single trace, but only on the set of all the possible traces a given system can generate during execution.