It is the domain
$$Q_T:=\Omega \times (0,T)$$
where $\Omega \subset \mathbb{R}^n$ is the space domain, which shall be bounded. Now it depends on the source whether the time or the space comes first; and whether $0$ and/or $T$ are included in the time domain. For example see Evans "Partial Differential Equations" at the beginning of Chapter 7 where he looks at evolution equations.
EDIT: The notation of cylindric is quite loose, it means $Q_T$ has a kind-of-cylindric shape. $\Omega$ does not have to be a circle or something, it shall just be a bounded domain in $\mathbb{R}^n$. For example in "Partial Differential Equations in Action" by Salso on page 32 the following is an example of a space-time cylinder:
![enter image description here](