As far as what "know" means, hear is some commentary
from John Gill.

on jer 31:34
Quote
"for they shall all KNOW me, from the least of them unto the greatest of them, saith the Lord: not all mankind; but all the house of Israel, all the family of God, all the children of God being taught by him; not all alike, but all with the same kind of knowledge. This is frequently applied to the times of the Messiah by the Jews"

and on Heb 8:11
Quote
"for all shall know me, from the least to the greatest; from babes to fathers in Christ; not with a natural, but with a spiritual knowledge; not with general knowledge of him, that he is, but with a special knowledge of him, that he is theirs; not with a legal, but with an evangelical knowledge; not with the knowledge of him in, and through the creatures, but in Christ; and that not speculative, but experimental; such as is attended with faith in him, fear of him, love to him, and a cheerful obedience to his will: the knowledge of the Lord, under the New Testament dispensation, is greater than under the former dispensation; the subject matter of it is more distinct; God is more known in the persons of the Father, Son, and Spirit, in the perfections of his nature, in his titles and characters, and in his Son; the manner of it is more clear, open, and perspicuous; the persons to whom it is communicated are more numerous; it is not restrained to Jews, but is given to the Gentiles; and all this owing to a greater effusion of the Spirit; see 1Jo_2:27."