An expectation is a strong belief that something will happen or will be the case.
When we talk about expectation design in the context of the organization, we are talking about the awareness and deliberate action of articulating clear and fair expectations of various role holders within the organization.
Expectations that are slowly and iteratively revealed as a part of unsatisfactory deliveres (the "Just do it and I will tell you how it sucks" approach) often cause frustrations on behalf of the expectation holder and demoralizes the performer.
Expectations should be thought out and cleary communicated ahead of time to avoid the performer having to fall on their face again and again.
Unclear expectations facilitate misunderstandings, and what can be misunderstood will eventually be misunderstood.
Praciticing this skill means ensuring that new team members unfamiliar with unwritten rules can easily conform to expectations, and that it is clear when one is performing within and outside the perimeters of an expectation.
Making sure expectations are familiarizable means having some sort of mechanism where the person expected to adhere to the expectation can reflect on and communicate their level of familiarity and comfort with the expectation.
For a more in-depth perspective on the concept of familiarity with expectations, check out this article.