What does John 10:37-38 mean?

37 If I do not the works of my Father, believe me not. 38 But if I do, though ye believe not me, believe the works: that ye may know, and believe, that the Father is in me, and I in him. (John 10:37-38 KJV)

William Burkitt’s Commentary

Here we have a second argument, by which our Saviour proves, that it was no blasphemy to call himself God; but that he was God in very deed; namely, an argument taken from his works: If I do not the works of my Father, believe me not; and the argument runs thus; If (says Christ) I do those miraculous works, which no power less than a divine power can effect, then you ought by these works to be led to believe and acknowledge, that I am truly and really God: but the works which I do are the effect and product of an omnipotent power, therefore you ought to believe, that I am one in essence with the Father, there being a mutual in-existence of one person in the other, so that he Father is in me, and I in him; and thus I and the Father are one.

Learn hence, That Christ never required of his disciples and followers an implicit faith, or a blind obedience; but as he submitted his doctrine to the trial of reason, so he submitted his miracles to the examination and judgment of sense: therefore he says, If I do not the works of my Father, that is, divine works, believe me not to be a divine person.