what is it?
There are lots of opinions about the KoG. We have lots of Qs. 
Let's work from simple to complex.
DEFINE IT
Again, working from simple to complex, before we try to define the KoG let's define 'kingdom.' What is a kingdom?
king + domain = 
a king's domain
is God's Kingdom really REAL?
or just an imaginative notion?
Any EXPECTATIONS that this King would be ACTUAL?
Yes, - see the most quoted OT passage in the NT
Psalm 110
The LORD says to my Lord: 
      “Sit at my right hand ..."
reminder:
God is distinct 
from His Creation.
He rules His Creation from without and within.
The Kingdom of God
Keeping our focus on 'the King' we need to ask, "Is God really (literally) a king or not? ACTUALLY a king?"
YES - He is the Creator Owner...
{Heb 1:1-2, "He made"}
                               ...AND the Trinity sent 
                the Son as a Missionary 
INTO His Domain (Creation) to RESTORE it.
        > > > you included

                         see John 3:16 & Phil 2:5-8
Oneism vs. Twoism
{The Architect is not the same 
thing as the walls and rooms
he designed - C S Lewis, Mere Chr.}
What is the TIMING of God restoring His Domain?
The King's First Advent 
!
God calls Himself "King"
     see Malachi 
1:4 LORD of Hosts,
1:6, honor, respects
1:14 King 
2:10, Father, Creator
2:8, Owner
2:10, Source

a simple syllogism:
A - God is King
B - Jesus is God
A+B - Jesus is King
Jesus came announcing His Kingdom and its Gospel. He bought it back at the price 
of the Cross. Then, He returned to His rightful Throne. He is building up and restoring His Domain NOW.
{Heb. 1:3, "sat down at the right hand of the Majesty..."
The Royal Imprint
Jesus has left us many markers of His Sovereignty. Here are just 2:
Melchizedek 
and Omega - see Rev. 1 
JESUS like 
Mel
is BOTH
King 
& 
Priest
The Alpha
Jesus is our Priestly KING NOW.