Tests like GRE GMAT and TOEFL are referred to as Standardized tests. The standardized test is the only uniform benchmark that can be applied to all applicants. US Universities get applications from all over the world and it is difficult to accurately compare the academic record from two different academic systems. Standardized tests provide some insight into an applicant's intellectual preparation. For any degree program, the tests are one of many parameters for admission. A good score helps overcome other wesk aspect(s) of the applicant. Similarly if an applicant has stellar academic recors from a reputable institution then the standardized scores become less significant and it is ok if the score is somewhat low.
Depending on your target degree program, you may be required to take one ore more of the following tests
GRE General Test
is required by most of the Graduate Programs (MS and PhD). GRE Subject test is also available in eight specialized fields, but for most cases you can manage your admission with the GRE General Test score.
GMAT (Graduate Management Admission Test) is required for MBA program and some MS programs.
SAT score is required for undergraduate programs
LSAT (The Law School Admission Test) is the test for admission to the law schools
TOEFL (Test of English as a Forign Language) is a test of English, which is required of applicants for whom English was not the first language. Some of the programs require TOEFL on the basis of Citizenship. Some other programs consider if English was the language of teaching at your previous degree program.