Recommendation letters indicate to the admissions committee that individuals who know you think you will do good work in graduate school. They also validate some of the things that you declare in your CV and in your “Statement of Purpose” essay. Often a selection committee will use the numeric information (GPA, GRE) to rank the applicant pool. Then they look at a group of the highly ranked candidates and eliminate from further consideration any candidate who does not fit well with their program (based the Personal Statement Essays). Final decisions often come down to looking at recommendation letters for the most convincing endorsements.
It is common practice to waive your right to review the letters. The US Federal Educational Rights and Privacy Act of 1974 (FERPA) gives enrolled students the right to view the contents of their application files. By waiving this right, your references are likely to be more candid in their statements about you. Some references may refuse to submit a letter when they learn that its confidentiality is not guaranteed.
Once you have been accepted into a program, as a courtesy you should send thank you letters to people who wrote you recommendation letters or helped you in the application process.