Short answer:

Because it was by far the biggest and most industrialised one. Especially Auschwitz II (the one with the direct train line) was feared because it was one of the Vernichtungslagern (extermination camps), therefor less of a labour camp and more of an execution factory, complete with sorting on arrival by "can be worked to death" or "take a shower first". There are stories from inmates that tell that during the final years of Auschwitz, the crematories were in such frequent use that the entire area experienced a constant powdering of flakes of human ashes.

Also, Auschwitz III, which fortunately was never finished, would have dwarved the horrors of Lager II by sheer size and determination.

There are a few reasons Auschwitz has the fame it does. It was the biggest of the camps, and it also killed more people than any one camp. However, it killed proportionately less people than some of the other camps. Timothy Snyder makes the case that Treblinka was actually more efficient as a death camp. This means that Auschwitz had more survivors, both in real numbers and per capita, than others.

Also, many of Auschwitz's survivors, particularly Eli Wiesel, were from Central or Western Europe, rather than Eastern Europe. These countries after the war (and the United States, where many survivors fled) enjoyed greater freedom of expression after the War. In Eastern Europe, the near-eradication of the Jewish population was subsumed but the Soviet mythology of the Great Patriotic War, where, in good Communist fashion, all people had suffered alike. These survivors helped craft a narrative where Auschwitz was the center of the Holocaust, though it was actually further West and arguably slightly less terrible than the horrors east of Poland.

The short answer as to why Auschwitz looms large in historical memory as the epicenter of the Holocaust is twofold. Firstly, and perhaps counter-intuitively, one had a greater chance of surviving being sent to Auschwitz than the other Operation Reinhard camps. This was because Auschwitz was a hybrid work-death camp. There were large industrial plants adjacent to the camp. The SS administrators had need of slave laborers and Jews that somehow had skills necessary could be selected to work. While the other death camps also selected able-bodied workers, the need for them was less acute. A chemist like Primo Levi had more value alive than dead. This selection process was notoriously fickle and being selected for work often meant daily brutality and starvation. Furthermore, living meant being in the presence of the mass murder of those who were not selected, adding to the nightmarish quality survival.

The second reason is that Operation Reinhard climaxed at Auschwitz in mid-1944 with the extermination of Hungary's Jews. Hungary was a German ally and held off on German demands to export its Jews as an issue of national sovereignty, but when the Germans put increased pressure on the Hungarian government 1944 when it became apparent that the Hungarians were sending out peace feelers to the allies. The Jewish population, which composed both of Hungarian Jews and other European Jews that fled to Hungary as a shelter, found itself in acute danger. The Aktion lasted from May through July 1944 and was one of the few times the extermination apparatus operated at full capacity.

For more information, Timothy Snyder's sections on the Holocaust in Bloodlands is an accessible account on this. Also, /u/TRB1783 also give an excellent answer in this thread.

Ninja Edit: It also occurs to me that one of the reasons that makes Auschwitz a relatively unique camp within Operation Reinhard is that it was the only death camp that was in the Reich proper. The Third Reich annexed this area after the conquest of Poland and incorporated it into upper Silesia. Therefore Auschwitz is a microcosm for the Third Reich's various population policies. This included the Germanization of the surrounding land, reclaiming the area for Germany and building modern settlements and factories. The SS intended Auschwitz to be a "model town" of the new order in the East. This entailed the ethnic cleansing of the Polish inhabitants and many ended up in Auschwitz as laborers and local Jews exterminated. This also means that the experience of Auschwitz mirrored much of the Third Reich as a whole and dovetails with the form that people expect a Third Reich concentration camp to take.

First of all, there is a difference between concentration camps and extermination camps. Concentration camps used forced labour to support the war effort, eventually killing those that couldn't work anymore. Extermination camps were just what their name makes dreadfully clear. Most arrivals were immediately killed.

What made Auschwitz II-Birkenau (the actual extermination camp, there was the Stammlager Auschwitz I, initially used mainly for political prisoner and later POW, as well as Auschwitz III-Monowitz, mainly used for forced labour) stand out was the sheer number of people murded there, estimated at 1,1 million, 900 thousand of which right at their arrival.

For the people who weren't killed outright, I have no idea if the conditions were worse than in any other camp, but I remember from my visit how the guide talked about the abhorrent conditions specifically of the "Zigeunerfamilienlager", the site for Sinti and Roma families. But again, I doubt one can quantify the horror, or compare the conditions of living in one camp to another, especially in the occupied east.

This is a very good question. The usual answers are "because it was the biggest camp" or "because most people died here", but that is only part of the answer.

When "Auschwitz" and "concentration camp" are used in context, this usually refers to the extermination camp, which was one part of Auschwitz. The actual "concentration camp" was separate from this and held prisoners that were not killed immediately, as those in the extermination camp were.

The extermination camp was called Auschwitz II Birkenau, and between 1.1 and 1.2 Million people were killed in its gas chambers. From the sheer number of people killed, Auschwitz is the most, well, prolific killing center.

That is a good reason why Auschwitz could be considered the "worst" concentration camp. However, the truth is more complicated than that.

The other 4 main extermination camps (Belzec, Sobibor, Treblinka and Chelmno) were pure extermination camps. They did not have a concentration camp compound to them. They were very small, because no prisoners had to be housed here, there were no factories where they would be put to work.

These camps were built near the large Polish ghettos, where the Jews of Poland had been forced to live. Being pure extermination camps, the numbers of survivors from these 4 camps is just a few hundred. Trains would come in, unload their prisoners, go back to the cities for the next trip, while the unloaded victims were killed.

Over 2 Million people were killed in these 4 camps, and only a few hundred survived. The camps existed only to kill the Jewish population of the nearby ghettos.

When their grim task was fulfilled, they were demolished. Everything was destroyed, the mass graves were dug up, corpses burned, ashes scattered. Nothing was to remain of the horrors that happened here. So, given the low number of survivors, as well as the camps' destruction, which was accomplished long before the end of the war, these camps are simply far less well known than Auschwitz.

Auschwitz was captured mostly intact, and was survived by some 60.000 people (again, because it was a concentration, as well as an extermination camp).

This has further consequences. With so many survivors from Auschwitz, there's many more people to tell the story of that camp, leading it to be much more prevalent as a cultural symbol afterwards.

Almost fifty years after Auschwitz, the story of Auschwitz, as seen through the eyes of a German industrialist, became a movie called "Schindler's List". Spielberg's film shed light on the plight of the victims of Auschwitz, again confirming it as not just the most lethal, but most well-known camp.

And in this case, most well known equals being considered the "worst".

By the way, there is a surprising reason why Auschwitz was the most lethal camp, and it has nothing to do with the fact that it was the most industrialized. For most of the Holocaust, the deadliest camp was Treblinka. Between 750.000 and 950.000 people were killed here. Auschwitz only surpassed that number in the summer of 1944. What had happened? Germany had invaded Hungary, a former ally, and home to a large Jewish population that had so far escaped the Holocaust. Being under German control now, they were to be exterminated. But by this time, Treblinka and the others had been destroyed. Auschwitz was simply the only camp left.