In Hebrew heaven is shamayim. The word is always plural. The Scriptures seem to indicate that there are three heavens by which may be referred to in writings: the immediate atmosphere of the earth, the area above that of the stars, moon, sun etc, and the outer area where God is said to dwell. The Apostle Paul alludes to this when he states that he was caught up into the "third heaven" and saw "unutterable things". Paul saw into the throne room of heaven much like Isaiah, John and others.
The Hebraic understanding of heaven is not what Christians have traditionally imagined as this ethereal place where we will one day be "caught up to in a rapture", but it refers to the Messianic Kingdom ON EARTH when God (Messiah Yeshua) will dwell with us for 1000 years; afterward ushering in the Renewed Heaven and earth where all sin and evil has been eradicated. At this time God will dwell with mankind as He did in the beginning before sin entered the world. When Yeshua said that the righteous shall "inherit the earth" this is the time period that He was referring too.
As a side note: since ancient times Jews have not liked speaking the Name of God so they used substitutes for The Name like: HaShem, Adonai, Elohim, and even Heaven. Hence, the Kingdom of God and the Kingdom of Heaven are one and the same - The Kingdom of YHVH.
I hope that this little lesson has added clarity to the Jewishness of Yeshua, His first disciples and the New Testament writings.