To leave out is to fail to include something. It should have been there and it is not.
It splits round an object. The omission may be accidental or deliberate, and only the context tells you which, which is why being left out of a list is a complaint and being left out of a team is a decision. There is a strong emotional sense too, since feeling left out is the experience of not being included socially, and it is one of the plainest phrases in English for a real hurt.
Practised in Phrasal Verbs