The Fourteenth Amendment was issued on July 1868 in the Reconstruction period. It legally guarantees same citizenship rights that will be equally protected by law for all US citizens. It was written as a reponse to the issues that were taking place at the time with the situation of former slaves, as most of them were black and suffered racist discriminations.
The legal text is aimed to eliminate discrimination that may affect a US citizens, not only because of his/her race but due to any other factors too: gender, religion, ethnicity, sexual orientation, socioeconomic situation, etc. Nowadays, the LGTI movement stills claiming for their equal rights and for the end of homophobic attitudes and even agressions. Therefore, the legal text which provides the legal basis to fulfill their complaints is actually this 14th Amendment.