When talking about politics, world peace or international trade, "state" usually means the same thing as country or nation. We sometimes use the word "state" to mean "the idea of a country", for example, "Should the State allow people to say whatever they want, or should it try to control what people say?"
"State" can also mean "a section of a country". Some countries use different words for sections of their country, such as province, prefecture, or district. Many countries define themselves in their own laws as being made up of two or more states.
Mexico, Germany, Australia, and the United States of America are examples of this kind of country. They are usually called federal republics. In this type of country, the country has a central federal government that is responsible for making and enforcing the important laws that keep the whole country safe, and carrying out the special functions that only a country can do, like printing money or running an army. But in countries of this kind each state also has its own state government responsible for things inside this state, for example, how schools are operated and what roads need to be built. Each state has its own legislative body, and also chooses people to represent the state in the national legislative body.
Any two states in the same country may have very different laws about how certain things should be handled. A state full of dry, flat places like Texas will have very different laws about farms and water supply than a state such as Florida where the ground is very wet. A state surrounded completely by land, such as Utah, will not have any laws about fishing for tuna, but a state consisting of small islands in the ocean, like Hawaii, might have many laws about fishing for tuna.
Because of these differences, many people think natural borders (like mountain ranges and rivers) may be more useful than the political borders left by history. The theory of this is called bioregional democracy.