I'll tell you.
Long before corrugated fiberboard (what we generally call a cardboard box), soap (among other things) was actually transported in sturdy wooden boxes. Because everyone needs soap, there was a proliferation of these boxes in any given town. They were surprisingly sturdy, easy to find, easy to move (when empty), and, therefore, provided the perfect platform for street speakers.
Street speakers, which, I imagine, have been around since the first human being realized not everybody agreed with him and he was hell bent on "educating" them, would start talking to passersby about whatever topic they felt strongly about. As people would stop to listen, the crowds would get bigger and it would be harder for people to see or hear the speaker. The speakers, wanting the largest number of people to hear the message they thought was so important, would grab a soap box and flip it over to stand on it. The extra height put the speaker above the crowd and allowed them to stand out from the rest of the people and project their voice more effectively.
Street speakers were often people talking about political issues, and crowds could get a little rowdy, so law enforcement officials were usually on the ready, waiting to break up a fight or a riot. The large crowds could also spill into the streets and cause traffic problems. So, while the street speakers felt that the first amendment gave them every right to stand on their soap box and say whatever they pleased, they were always at odds with police, who were trying to ensure crowd control.
Street speakers, or soapbox orators, reached the height of their popularity in the decades (yes, decades) just before World War I. Many people didn't have a lot of discretionary income to spend on entertainment, and these soapbox orators were a source of entertainment. Free entertainment. And they generally worked hard to entertain the crowd and keep their attention.
Of course, with so many soapbox orators, you can imagine that some of them were on the opposite end of the political (or even religious) spectrum. Sometimes part of the crowd's entertainment was found in two sparring street speakers, each stating their own message while also heckling the other. This, again, generally led to a rowdier crowd, and sometimes even lead to physical violence. As previously stated, law enforcement officials did not look kindly upon soapbox orators.
Eventually, street speakers fell in popularity, and radio personalities gladly took their places. And, even the soap boxes were changed to the cardboard we know today. So there you have it, the origin of the phrase "up on their soapbox." The phrase is still alive and well, but all that inspired it has long since disappeared.
Now the phrase is only used metaphorically, to describe someone who is speaking very passionately about something, and many people consider a blog a "soapbox". I am passionate about a lot of things (I don't do anything halfway. If you're gonna do it, do it right), so I chose the name for my blog accordingly. This is my soapbox. Of course, I added the space back in (so soapbox is no longer one word, but two), well, because I felt like it. Being on a soapbox has more to do with passion for the subject, than the reasonableness of that subject, in my opinion.
So there it is. You have been educated. Congratulations.