Auschwitz is well known in large part because some people actually survived their imprisonment there. As a part of the larger complex which included Birkenau, Auschwitz was the camp at which prisoners who were still judged to be capable of productive work were held. Though their captors held no regard for their well-being, the fact that their labor could be rented out to nearby chemical factories meant that there was at least some use to preserving their lives. Birkenau would also become a place where prisoners were held before being transferred to labor in some industry in Germany. The fact that a (relatively) large amount of prisoners passed through Auschwitz and Birkenau on their way to other destinations increased the pool of people who could survive the two by virtue of dispersion. It’s a grim way to understand it, but we know very little about life in some other camps by way of the fact that there were very few (as in single digits) or no survivors from them.

The group of camps clustered around Auschwitz is also further distinguished by the fact that it continued operating far later in the war than other similar camps like Belzec, Sobibor, and Treblinka. When the Red Army came across the ruined ground on which those other three had stood, all they found was a hasty attempt at covering up what had gone on. At Belzec, for example, when the German authorities found no further use for its murderous apparatus, they demolished all the buildings, tilled the land, and planted an orchard in an attempt to disguise its purpose. At Treblinka, as the Red Army approached, the guards shot the remaining three hundred prisoners and then evacuated so that no living soul remained.

At Auschwitz and Birkenau, on the other hand, the prisoner population was still too large for the guards to deal with, and they were too scared of the speed with which they might be overrun for them to systematically murder the remaining inmates and destroy the camp as the Soviets approached. So, they killed some, left others, and then forced the remainder westward on a grueling death march. The last were fairly common at the end, as the weight of insane procedure compelled the Nazis to move their victims further and further into their territory as said territory shrank. And, as brutal as those marches were, they at least afforded prisoners an opportunity to escape by slipping away from the column or even feigning death. Ruth Klüger is one survivor who lived to tell her tale as a result of one such lucky escape.

Further, the fact that prisoners like Elie Wiesel and Primo Levi were left behind in the camps meant that there were actually live survivors to be found when the Soviets broke through the gates. The first footage we have of the realities of the Holocaust was filmed at Auschwitz, and then broadcast worldwide.

Consequently, although more than ninety percent of the prisoners who passed through Auschwitz and Birkenau were murdered, that rate of survival is higher than other death camps. From Treblinka and Sobibor, for example, there are only one hundred and twenty five known survivors. It's surreal to say, but the Jews who were imprisoned at Auschwitz were lucky in the sense that they had generally been found and captured later in the war, and therefore had a greater chance of surviving. It's an absurdity which Primo Levi speaks to in his memoir “Survival in Auschwitz.” In that and other of his writings, he reflects on the fact that the world lost moral meaning in the gray zone of living amidst death. Perhaps by some perverse logic, the indignities of slavery saved many of the survivors from Auschwitz and Birkenau.

Ultimately, Auschwitz is best known because among the death camps, it is the one from which the most survivors were able to tell their stories. And, one place where they told those stories was sure to garner widespread attention. When Hans Frank and his accomplices were captured and tried at Nuremberg, all the details of Nazism’s sick annihilatory ambition were spilled into public view. Contemporary reporting by the New York Times noted each new detail and testimony in the case, and how the task of the prosecutors was to transform the sensational horrors that were recounted therein into a record which would meet “the firm test of justice.” The trials captivated many people around the world, and for those who followed them, it is the name Auschwitz which became most closely associated with the Holocaust.

So, while there were also other camps like Dachau and Theresienstadt from which (relatively) many people survived, they are again distinguished by the fact that they were not built for the purpose of murder as the death camps were. Because of the difference in intent, Auschwitz is unsurprisingly more notorious.

There is also, a final point that I think should be made about the actual timeline of the Holocaust, and it is not commonly understood. I think it also speaks to the foundation of your question.

The majority of the killing did not occur in the camps that we are most familiar with, but rather on the trackless plains of Belarus, Poland and the Ukraine. It was there that otherwise ordinary men took up arms against civilians whom they had never known and shot them. Millions were killed not in the gas chamber, but with common lead. Millions more were simply starved to death while confined by wire to open fields without food, shelter, water, or sanitation. By the end of 1942, three quarters of the six million Jews who were eventually killed were already dead.

Edit: I corrected a factual inaccuracy.