"His wife was of Chinese ancestry."
What does it mean by "was of"?
"His wife was of Chinese ancestry."
What does it mean by "was of"?
Was denotes past tense, and of is a preposition. 'Was of', together, denotes that the person's wife's ancestors were ethnically Chinese.
However, it is possible to make the sentence clearer. If the person is still married to his wife, and she is living, it would make far more sense to say "His wife is of Chinese ancestry". If she had passed on, one could say "His late wife was of Chinese ancestry"
If a person is no longer married to his wife, or his ex-wife is deceased, one could say "His ex-wife was of Chinese ancestry", and "His late ex-wife was of Chinese ancestry".
One could replace "of Chinese ancestry" with "ethnically Chinese", in case the person in question had exclusively Chinese ancestry.
Saying something like "His wife has/had Chinese ancestry/heritage" usually implies that the person has Chinese ancestry in addition to non-Chinese , though it depends on the exact context.
It is important to understand that of has several implications. One of them is belongingness.
His wife was of Chinese ancestry.
The wife's cultural background and/or her mind-set and/or behaviour are framed by Chinese ancestors and/or their Chinese way of living, thinking, upbringing, etc.
Here 'of' is used to demonstrate 'belongingness' - that something is not necessarily part of something BUT strongly permeated by something else and implies that certain features are shared between the 'something' and the 'something else'.
As an example, you could say 'I from Switzerland but I am not of it', which would imply that you are Swiss but that you have not been framed by or that you not necessarily advocate Swiss culture, values, thinking, way of life, etc. Another example would be 'I am a man of good manners.'
Contrarily, in formal English there exists the phrase be of service, which is considered idiomatic (according to the Cambridge Dictionary). Here 'of' is used to demonstrate 'is'/'are'. If somebody is 'of service' to somebody he/she is helpful to somebody. Other examples are 'John is of great help to us.'.
I strongly recommend the book English Prepositions Explained by Seth Lindstromberg. It explains prepositions like no other.
Last but not least, 'be of service' is referenced in Cambridge Advanced Learners Dictionary.