The Final Solution was the culminating step in Hitler's plans towards Jewish people. Simply put, the "final solution" was the extermination of the Jewish race. As Hitler had made more laws that were meant to target those of the Jewish faith, relegating them to greater peripheral status, Hitler had issued a "warning" that if Jewish individuals "led" to another World War involving Germany that Hitler would "deal" with it in a finalizing and totalizing manner. In the early 1940s, this became translated as "the final solution," authorizing the complete extermination of all Jewish people. Consider how others in the Nazi party viewed the dimensions of the Final Solution:
As for the Jews, well, I can tell you quite frankly that one way or another we have to put an end to them. The Führer once put it this way: if the combined forces of Judaism should again succeed in unleashing a world war, that would mean the end of the Jews in Europe... I would therefore be guided by the basic expectation that they are going to disappear. They have to be gotten rid of.
When we speak of the Holocaust, the idea of ensuring that the Jewish people would "disappear" is one of the fundamental precepts involved in the Final Solution. In this declaration of the "Final Solution," Nazi Germany becomes synonymous with some of the worst crimes in human history.
The "Final Solution" was the Nazi term for the extermination of the Jews. The term "Final Solution" is short for the phrase "final solution to the Jewish problem."
To the Nazis, the presence of Jews in German territory was a problem. The Nazis believed that Jews were an inferior "race" whose presence would lead to the decay and eventual destruction of German society. Because of this, they wanted to get rid of the Jews.
There were a number of ideas proposed and methods tried for getting rid of Jews. These included ideas such as forcing Jews to emigrate to Madagascar and methods such as simply shooting Jews, as was done by the Einstazgruppen in Eastern Europe. However, none of these was satisfactory, for various reasons. Eventually, the Nazis hit upon the system of extermination camps. This, they believed, was the final solution to the Jewish problem.
I assume you mean "The Final Solution to the Jewish Question," which was the National Socialist plan to exterminate all Jews from Europe. Anti-Semitism had been rampant in Europe, especially Germany for many years before the Nazi's gained power. A number of attempts were made to keep Jewish people as subservient as possible; including the famous Nuremberg Laws which prohibited Jews from practicing professions and revoked their German citizenship. During the Krystallnacht riots, Jewish stores were vandalized and property destroyed. Plans to rid Europe of Jews originally involved deporting them to either Israel of Madagascar, as long as they were gone. When this was determined to be unfeasible, the plans for a "final solution" were drawn up at the Lake Wansee Conference outside Berlin. Jews were transported by railroad to camps, some to work, others to be executed, first by firing squad and later by lethal gas. Those who could not work were executed immediately; those who could work were put to work in a variety of functions until they were too sick or exhausted at which point they also were executed. The details are too exhaustive and have been written about too extensively for further commentary here. You should have no problem finding extensive information on the Holocaust.
The implementation of the Final Solution brought about the slaughtering of millions of Jews. Heavily armed mobile killing squads were used to eliminate all undesirable elements, including the Jews, in German-occupied territories. The Germans sought to exploit as much as possible what all these victims had materially before getting rid of them. People were stripped in masses, humiliated and intimidated so as to prevent them from fighting back before being gunned down. As it became increasingly clear that there were simply too many Jews to be killed through the mobile squads, the Germans turned to an extreme policy of mass extermination and industrial killing through the establishment of death camps to get rid of the Jews. Such an aim was singled out as the top national priority - Jews were rounded up, transported to factories, where an industrial scale of technology was to be used to kill them all. The technological breakthrough was to use rat poison to kill the Jews in large numbers, which greatly increased the numbers that could be eliminated. Corpses were cremated and buried in mass pits by prisoners to relieve the strain on German manpower.