This is going to be a long and complex answer. I don't know if you realize it, but your "simple" question is not simple at all.
The oldest universities in the United States were established for religious purposes. Harvard College and Yale College were established in Massachusetts and Connecticutt to provide education to young men who wished to be ministers of the Congregational Church. In history texts, you will find the people who established those colonies (Massachusetts and Connecticutt) referred to as Puritans. Their church has become known as the Congregational Chruch. They established those colleges to educate ministers of their religion. In the more than three centuries since they were established--Harvard was established in 1636, and Yale was established in 1701--they have grown to be very large and prestigious universities. Addtionally, Harvard University is one of the most respected research institutions in the world.
Other colleges were established to provide a general, liberal arts education for young men. A noteworthy example is Princeton University. Originally, the College of New Jersey was established to train Presbyterian missionaries, and was located in Elizabethtown, New Jersey, in 1746. It had funding problems, though, and the colony agreed to help finance the institution if it were opened to general enrollment. It was moved to Princeton, New Jersey, and was renamed Princeton University in 1896, although it was referred to as "Princeton" long before that. It is one of the eight "Ivy League" universities. You can read about the Ivy League,
if you click here.
You will note that i have referred to men only. Most (but not all) of the Ivy League schools were originally founded by churches in order to educate the young men who would become ministers of the religion which had founded the college. This is no longer true, to the extent that they have open enrollment, and accept anyone who can afford to study there. All of these universities are now still private, but no longer affiliated with any particular religion. No one thought about giving women a university education.
But many people wanted to educate women--usually it was women who wanted women to be educated--so that several colleges were founded which were for women. They are called "the Seven Sisters" of the Ivy League. Two of them, Vassar College and Ratcliffe College, now accept men for enrollment. The other five still function as women's colleges. You can read about the Seven Sisters
by clicking here.
On many other occasions, colleges were established by men who were eager to provide a good education for their sons. Many have since grown to be major universities. Many were estalished by religious groups, and, for example, Notre Dame University was established to educate young Catholic men, and is one of the most prestigious universities in the country--it is still a Catholic institution, but those who enroll are not required to espouse the Catholic faith.
Others were established as secular institution, and one of the most common means of doing so was the "land grant" university. That means that a private individual, or a state government, provided land upon which to build a university, as a means to inspire the foundation of an institution of higher education. Two examples from the state of Illinois can serve as examples. The Illinois State Normal College was founded in 1857 by Jesse Fell, who made a grant of land for the purpose. Jesse Fell had been a campaign manager for Abraham Lincoln, and he was able to attract several wealthy and influential men to help establish his university. The word "normal" in the title refers to
école normale, a French term which means a teacher's college--a place where one teaches young men (and now women) to be teachers. A railway station was established near the college, and is now the town of Normal, Illinois. It became Illinois State Normal University, and is now simply Illinois State University.
The University of Illinois was established in 1867 as the Illinois Industrial University at Urbana, Illinois, using the Morrill Land Grant Act of 1862, which provided land for universities in the western states. (Now considered a part of the Midwest, Illinios was at the western edge of most of the states of the United States in 1862--to the west were very few states, most of the land being territories governed by the Federal government.) It became the University of Illinois. The railway built a station nearby, which was called College Station, and which is now Champaign, Illinois (Champaign and Urbana are in Champaign County, Illinois). Today, it is the main campus of the University of Illinois, and is officially know as the University of Illinois at Urbana-Champaign (which aggravates the citizens of Champaign, who tend to call it Champaign-Urbana). There are now two other campuses--the University of Illinois at Chicago, and the University of Illinois at Springfield.
Such landgrant universities have prospered, as they are supported by the governments of the states in which they are located. The University of Illinois at Urbana-Champaign, for example, was given two billion dollars by the State of Illinois in the last year that i worked there (1981). Other notable examples are the Ohio State University, Michigan State University, the University of Michigan, Pennsylvania State University--these are all part of the "Big Ten," which is a group of
eleven universities. You can read about the Big Ten
by clicking here.
There are, literally, hundreds of land grant universities--most major universities in a state system have many campuses and institutions. The University of Illinois at Urbana-Champaign is a world renowned research institution, but it is only one of many universities supported by the state of Illinois. There are also Southern Illinois University (which has three campuses just as the U of I does), Sangamon State University, Northern Illinois University, Easter Illinois University and Western Illinois University. Both New York and California have extensive university systems, with many campuses and separate universities.
And that only scratches the surface, because there are so many private colleges and universities, and other types of state supported schools--liberal arts schools, A & T (agriculture and technology schools, which can be private or state-supported), A & M (agriculture and mining), "Tech" schools such as Georgia Tech, a technology university supported by the state of Georgia. There are many religious colleges and universities in the country, which accept enrollment from people who do not practice their religion, but which are supported by the church which founded them. A good example is the Wesleyan system. John Wesley was the founder of the Methodist religion, and the Methodists have established many Wesleyan universities, such as Illinois Wesleyan University, which is located in Bloomington, Illinois, right next to Normal, Illinois, where Illinois State University is located.
You did not ask a simple question.