A citation is a reference to a legal authority. Citations to legal materials follow a standard format so that the resources can be found by others. Citation formats exist for many different types of legal sources including cases, statutes and secondary legal materials.
When you are searching for cases, your most efficient search will be if you have the case citation. Regulations also have their own citations as well. They all tend to follow a similar pattern. The citations reflect the name of the source, which is abbreviated.
Volume Number - Source Abbreviation - Section or Page
517 U.S. 308 = 517th volume of the U.S Reporter, pg. 308
116 S.Ct 1307 = 116th volume of the Supreme Court Reporter, pg.1307
57 F.R. 41731 = 57th volume of the Federal Register, pg. 41731
If you are not sure what citation you are looking at, you can try searching Cardiff University's Legal Abbreviations Index (It covers case reporters and legal periodicals from the British Isles, the Commonwealth, and the United States).
Parallel citations are instances when the same case or statute has been referenced/reported in more than one source. For example, a landmark case like Roe V. Wade (where decision of lower court was affirmed but then part of it was reversed - which actually is not considered good law) might be cited as: Roe v. Wade, 410 U.S. 113, 93 S. Ct. 705, 35 L. Ed. 2d 147 (1973)
410 U.S. 113 = volume 410 of the U.S. Reporter, starting page 113
93 S. Ct. 705 = volume 93 of the Supreme Court Reporter, starting page 705
35 L. Ed. 2d 147 = volume 35 of the United States Supreme Court Reports, Lawyer's Edition, 2nd Series, page 147
This means that you can look in any of these reporters and find the same information reported. In the electronic sphere, if you go to Nexis Uni or Westlaw you could use any of those citations for your search and you would get the same search result.
If you wish to learn more about "BlueBooking," see:
The BlueBook is not the only style used in the legal world. This page from Harvard Law school describes the BlueBook and some alternatives.