Dear Brother Classic, A dispensation of God is something He has dispensed to us for a given time. For instance, we do not have the same admonition of not eating of the tree of good and evil which I personally believe to have been the law in part which is a ministration of death, and it killed.
A dispensation normally introduced a covenant God had with men. E.g., Zec 3:7 Thus saith the LORD of hosts; If thou wilt walk in my ways, and if thou wilt keep my charge, then thou shalt also judge my house, and shalt also keep my courts, and I will give thee places to walk among these that stand by. Although this was not the beginning of a dispensation, the following covenant was which is know as the age of promise. Gen 17:2 And I will make my covenant between me and thee, and will multiply thee exceedingly.
One such dispensation was given to Paul I Col1:25. Whereof I am made a minister, according to the dispensation of God which is given to me for you, to fulfil the word of God;
Col 1:26 Even the mystery which hath been hid from ages and from generations, but now is made manifest to his saints:
To my understanding there are seven such dispensations starting with Genesis through the Millennium.