Throughout the three Dragonball series and comic books, we constantly see this logo:

shot taken from this cel from Lovers of Juuhachigou

What the hell does it mean? Railroad crossing? Team Rocket? No, my friends. It is the symbol for the Red Ribbon Army. But what is that, you're asking? Well, I'll tell you.

The Red Ribbon Army was this big tyranical organization of sorts, run by a short man named Commander Red (this the "red" in "red ribbon"), who was collecting the Dragon Balls to wish himself to be taller. Everyone thought he wanted the Dragon Balls to rule the world, though, but that was not the case. The army was comprised of commanding officers whose names all involved a color of some sort, like General Blue, "Major Murasaki" (murasaki is japanese for purple), and Assistant Black.

Assistant Black was a very tall black man (as in African-American, not black-skinned like Mr. Popo) that served Commander Red, who would always get very mad to have Assistant Black standing next to him. Assisant Black hated his job and was one of the people who thought Commander Red was after the Dragon Balls to rule the world. He found out the real reason, however, and ended up shooting Commander Red in the head, then took over and renamed the army to the Black Ribbon Army. But Goku killed his ass. (lol)

Goku became involved with the Red Ribbon Army, I think because they had a Dragon Ball, which Goku was after, and because one of the army generals was holding the mayor of a village he was staying in hostage. I could be wrong, don't quote me. Anyway, Goku headed off to save the mayor who is being held captive in General White's muscle tower (he was terrorizing the locals, too, that bastard!), and ended up having to fight a boss on each level, much like that Bruce Lee movie. He eventually encountered an android, Number 8, who looked a lot like Frankenstein. Number 8 is the first android of the Red Ribbon Army to make an appearance. Originally, he is supposed to be Goku's enemy, but he has too nice of a disposition (kind of like Number 16 but a little less intelligent it seems). He is ordered to fight Goku, but refuses, and then is threatened to be blown up if he doesn't fight. Number 8 refuses to do so, saying he'd rather die than fight, and Goku, touched by all that, decides to protect him. They befriend each other and so with Number 8's help, Goku defeats every single person in Muscle Tower, including General White (again with the help of Number 8, who saved Goku's life at that point). The mayor is saved and all is well.

Goku gets more involved with this evil organization after the defeat (because he can't just walk away after kicking everyone's ass!) of Muscle Tower, fighting other RRA commanders and mercenaries (Tao Pie Pie, that is), and eventually travels to the army's headquarters. He proceeds to kick everyone's ass at HQ, right up to when Assistant Black kills Commander Red and takes over the army. Assistant Black tries to then kill Goku in his big mechanical suit (which for some reason is marketed as a toy with Number 17 piloting it), but Goku prevails and defeats Assistant Black, killing him by punching straight through him and the suit he was in.

This is where Dr. Gero comes in.

The doctor was one of the RRA's scientists, and I think from what we hear Bulma say when she happens to see him for the first time (in DBZ), he was a very good one too. But, you know, Goku had to come along and ruin all his plans. And it's the total and utter defeat of the whole army that makes Doctor Gero devote his entire life to destroying Goku. Since Dr. Gero himself is not strong enough to defeat Goku, he creates beings that are (or try to be). Number 8 was one his creations and the first to appear in the show, but after the defeat, he makes thirteen more artificial humans to off the exceptional saiyan. Each one of them carries the Red Ribbon logo on their clothing, with the exception of Cell...but he's a whole different story for another website.

That's all about what the Red Ribbon Army is from me. If you want more information though, check out this page at The Ultimate DragonBall Kingdom.