It is said (https://ncatlab.org/nlab/show/Tate+twist):
To return to our starting point, a crucial remark here is that whilst $\mathbb{Z}_{l}(1)$ is non-canonically isomorphic to $\mathbb{Z}_{l}$ as a $\mathbb{Z}_{l}$-module, the two are not isomorphic as Galois representations. Thus the presence of Tate twists is indispensable to the arithmetic aspect of cohomology.
What is the Galois representation of a sheaf? What is the arithmetic aspect of (étale) cohomology?