The Final Solution was the planned extermination of all the Jews in Europe by the Nazis, through systematic gassing. The implementation of the Final Solution after the Wannsee Conference in January 1942 can be explained by fundamentally, the core beliefs of Nazis and Anti-Semitism. Thus the Final Solution was also implemented because of Nazi obsession with solving the 'Jewish problem' which had failed in previous methods. The war, and in particular the German invasion of Russia had also created the foundation for the Final Solution of the Jewish problem.
Firstly, Nazi ideology had from the start of Jewish persecution in Germany and its occupied areas being the rudimental reason for Nazi actions including the implementation of the Final Solution. The Nazis believed that the Jewish race was of inferior blood contaminated the purity of their race. The Nazis, and in particularly Adolf Hitler, wanted a perfect race of Aryans. Jews did not fit into this perfect race.
This explains why the Nazis were planning to exterminate all Jews. The Nazis also had an anti-Semitic view that the Nazis were 'parasites' living on 'host' nations and that they would eventually try to take over the nation. This also linked to the idea that Hitler believed in that the Jews were involved in a conspiracy to dominate the rest of the world. Another part of Hitler's hatred of Jews was his linking of them to his hatred Marxism or Communism. The Jews were also blamed for everything that had gone wrong including Germany's defeat in WW1 as well as social problems. As leader of the Nazis, and the person making the primary decisions, Hitler's anti-Semitic views as outlined in his book Mein Kampf were very much a cause of the Final solution.
The Nazis also had 'scientific' socio-Darwinist reasons in their ideology...