In the previous verse, the Jews had accused Jesus of blasphemy, because he had said (John 10:30) "
I and my Father are one":
John 10:33: The Jews answered him, saying, For a good work we stone thee not; but for blasphemy; and because that thou, being a man, makest thyself God.
The author of John has Jesus respond by citing Psalm 82:6. First century Judaism was strictly monotheistic, so neither our author nor the Jews could interpret the Psalm as referring to the assembly of gods. Taken out of context, the citation implies that God had been describing all people as gods, in which case it could not be blasphemy for a man to speak of himself as the Son of God. Although Jesus has cleverly countered the claim of blasphemy, the Jews try to hold him, but he eludes them (John 10:39).
An inadvertent clue that the author was not a Jew is that he refers to "your law" but he was no doubt aware that the Psalms were not part of the Law, although he strengthens the case Jesus is putting by referring to it as such.