In Higher Education, Professor is the name of a particular rank of teaching staff. The precise importance of this rank varies. There is a broad difference between usage in the United States and that in Europe, and there is further variation between usage in individual institutions. You are advised to be cautious in using the title 'Professor' until you know the proper usage for the individual concerned. In particular, notice that the importance and prestige of a Professor may be different in American universities from that in British universities.
In Europe, the Professor of a particular subject was traditionally the head of the department. In early times, the Professor might be the only person actually paid to teach the subject - any assistant teachers were supported by being members of religious orders, and teaching as only part of their duties. (See also chair.) Benefactors endowed (~ gave a sum of capital sufficient to supply a perpetual income for) historic chairs. With increasing wealth, there came to be an increasing number of endowments, and there were often several professors in one department. These were the most highly paid members of the department, and to be appointed professor was the pinnacle of most academic careers. In recent years, there has been a growing tendency to award 'Personal Chairs' - that is, rewarding valued academics by appointing them as Professors, with that title and a suitable level of salary, without all the responsibilities, administrative and representative, of the traditional professor.
In the U.S.A. and countries who follow the American academic system, professor is a title given to most members of faculty, or academic staff. Assistant professors and adjunct professors are junior teachers who do not usually have tenure; in the UK, the equivalent are usually Research Fellows or Junior Lecturers. Associate Professors in the US may be Senior Lecturers or similar in the UK. Senior members of departments in American universities are full professors, and are roughly similar to traditional UK professors. Those with the administrative duties of British professors are sometimes called chair.
There is a note on spelling that you may want to see at Profession - professional - professionally - professor. A note on usage is at prof.
Beware too of a false friend: in French and Italian, the equivalents (professeur and professore/professoressa are titles of schoolteachers,
not teachers in Higher Education.