According to Black's Law Dictionary 2nd Edition we find numerous definitions resulting from case law.

license

Constitutional Law and Law of Contracts

Constitutional Law and Law of Contracts
A permission, by a competent authority to do
some act which without such authorization would
be .illegal, or would be a trespass or a tort. State
v. Hipp, 38 Ohio St. 226; Hubman v. State, 61
Ark. 482, 33 S.W. 843, Chicago v. Collins, 175
Ill. 445, 51 N.E. 907, 49 L.R.A. 408, 67 L.R.A. 224.
A permit or privilege to do what otherwise would
be unlawful. Palmetto Fire Ins. Co. v. Beha, D.C.
N.Y., 13 F.2d 500, 505; La Plante v. State Board
of Public Roads, 47 R.I. 258, 131 A. 641, 642; State
ex rel. Biscayne Kennel Club v. Stein, 130 Fla. 517,
178 So. 133, 135. Also, the written evidence of per-
mission.
A permit, granted by the sovereign, (emphasis added) generally for a con-
sideration (Smith v. Commonwealth, 175 Ky. 286, 194 S.W.
367, 370), to a person, firm, or corporation to pursue some
occupation or to carry on some business subject to regula-
tion under the police power. State ex rel. Guillot v. Cen-
tral Bank & Trust Co., 143 La. 1053, 79 So. 857, 858.
A "license" is not a contract between the state and the
licensee, but is a mere personal permit. Rosenblatt v. Cali-
fornia State Board of Pharmacy, 69 Cal.App.2d 69, 158 P.2d
199, 203. Neither is it property or a property right. Amer-
ican States Water Service Co. of California v. Johnson, 31
Cal.App.2d 606, 88 P.2d 770, 774; Garford Trucking v. Hoff-
man, 114 N.J.L. 522, 177 A. 882, 887; nor does it create a
vested right. State ex rel. Biscayne Kennel Club v. Stein,
130 Fla. 517, 178 So. 133, 135; Asbury Hospital v. Cass
County, 72 N.D. 359, 7 N.W.2d 438, 452.

So essentially, a license is permission from a sovereign to do some act. The state is not a sovereign nor is the federal government. We the people are sovereign, so why do we pay the government for permission to do an act?

This affects many things, like marriage, motor vehicles, businesses, liquor, construction and many more things.

Let's take a look at what the definition is for "Motor Vehicles".

License to operate motor vehicle is mere priv-
ilege, and not a contract or property right. Gar-
ford Trucking v. Hoffman, 114 N.J.L. 522, 177 A.,
882, 887; Blashfield, Cyc. of Automobile Law and
Prac., Perm. Ed., § 580.

Notice the decision does not speak to whom the license requirement might apply. It merely speaks to what a license is. Of course, it is not a property right. Of course, it is not a contract. Now you have proof that just because you got a driver's license you do not have a contract with the state. But this again only applies to those who fall under jurisdiction of the state and its statutes. It does not apply to people.

So a license is permission to do an act that would be illegal if the license was not obtained. What you have to know is to whom the license applies.