What is a state? How would one explain its origin and evolution?

At its basic level, a state can be defined as a nation of civilians living under a single type of government. Some states are autonomous (or sovereign), while others are not. Of the sovereign states, some are democracies, democratic republics (such as the United States), federations, confederations, or constitutional/parliamentary monarchies (such as the United Kingdom). A basic state is governed by an authoritative entity that promotes the welfare of civilians.
Basically, the state provides stability and processes by which civilians can benefit from goods and services produced within its borders.
Here is a list of types of government you may be interested in.
The origin of the state is derived from Plato's Statesman 302 c-d. Aristotle adopted Plato's conception of the state, which was said to manifest itself in six constitutional forms. The six forms are further divided into pure and deviant types.
Pure: monarchy, aristocracy, and polity (many rulers).
Deviant: tyranny, oligarchy, and democracy.
So, if the "pure" form of state is a monarchy, by extension, the "deviant" form of state is a tyranny. Here is how Aristotle defines the state in Politics, Book Three:

He who has the power to take part in the deliberative or judicial administration of any state is said by us to be a citizens of that state; and, speaking generally, a state is a body of citizens sufficing for the purposes of life.

Notably, Aristotle classified democracy as a deviant form of state. He argued that a democracy (much like tyranny and oligarchy) might originate from a foundation of violence. Aristotle warned that democracy could be manipulated for malevolent purposes by specific groups.

For tyranny is a kind of monarchy which has in view the interest of the monarch only; oligarchy has in view the interest of the wealthy; democracy, of the needy: none of them the common good of all.
For democracy is said to be the government of the many. But what if the many are men of property and have the power in their hands?

So, we can see that the idea of the state originated from both Plato and Aristotle. There are currently four theories of the state:
1) The Divine Right theory
2) Evolutionary theory
3) The Social Contract theory
4) The Force theory
It looks like you are interested in the evolutionary theory of the state. According to this theory, the state evolved from different forces that contributed to its origin: kinship, religion, force (war), economic conditions, and political inclinations.
According to Stephen Leacock, the "state is not an invention: it is a growth, an evolution, the result of a gradual process, running throughout all the known history of man, and receding into the remote and unknown past."
In other words, the state begins as an imperfect entity; through gradual processes (such as kinship, force, religion, etc.), human society is developed. From this, the state evolves towards greater stability, prosperity, and progress. Leacock proposes that the first states likely began as patriarchies or matriachies (the kinship factor). Aristotle agrees with this supposition of progressive change.
Aristotle believed that the state evolved from monarchy to oligarchy, from oligarchy to tyranny, and from tyranny to democracy. However, in hindsight, this evolutionary theory of the state only applied to the Greek city-states; it is far less applicable to our modern states today.
For more, please refer to the links below.
Source: Elements of Political Science by Stephen Leacock
http://classics.mit.edu/Aristotle/politics.html

https://plato.stanford.edu/entries/aristotle-politics/

https://www.marxistschool.org/classdocs/LeacockIntro.pdf