The story was really dumb and makes no sense. The question is, why has Stefano had it out for the Bradys for the last 20 years?
Technically, it started with Roman busting up Stefano's crime ring roughly 20 years ago, but it's since been retconned (retroactive continuity) that Stefano already had a beef with the Bradys for some reason unknown to them and Roman taking Stefano done for his illegal dealings was just the latest thing a Brady's done to piss him off.
It began in the summer of 2007, when Sami Brady and Lucas Horton were on their honeymoon, helping to build houses in New Orleans. They were working on a renovation of a building they discovered was Maison Blanche, Stefano's former residence in New Orleans where a lot of bad stuff went down in the mid-1990s. In taking down a wall, they found a box with a letter in it, written in Italian. The only word they could make out was Dimera.
Once back in Salem, they showed it to Bo and Hope Brady, John Black and Marlena Evans. Doug and Julie Williams just happened to return to Salem, and Julie could understand Italian a bit through her wordly travels. She read that it was a letter from Santo Dimera to his son Stefano, on Santo's deathbed. He was telling him that he had been in love with this woman and that the Bradys took her from him and that Stefano must make them pay. He then told Stefano that they could be found in America, in the town of Salem. The group learned the woman's name was Colleen. Caroline Brady heard this and noted that she had come across the name Colleen while going through some of her husband Shawn Brady's old things. She asked him about it, but he became upset and refused to talk about it.
Shortly thereafter, Anna Brady Dimera, Roman Brady's ex-wife and Carrie Brady Reed's mother, and Tony DiMera's ex-wife, came back to Salem and with her; she brought some letters that she had found with some of Tony's things. She was going to take them back to Tony, but thought they Bradys might want to read them, as it had something to do with them. Around this time a photo Colleen Brady was found, but she was the spitting image of Sami. It was then shown that Stefano's father, Santo, was the spitting image of EJ (with a cheesy mustache; and we'd learn much later, a bad Italian accent).
The letters Anna had were from Colleen to Santo; somewhere down the line, Tony had come into possession of them. They decided in order to get the whole story; they would need to find the letters Santo wrote Colleen. Rather than see if they could find them elsewhere first, they assumed that Stefano would probably have them in his possession. Bo and Hope went to the DiMera mansion and, with a little help from Steve Johnson, Hope snuck in and snooped around (the living room) and just so happened to find the letters under the sofa under the cushion of a chair.
Now, for whatever reason, both letters were in Italian. Never mind that Colleen came from humble beginnings and where she would have learned Italian (as she apparently did in the first place) is anyone's guess. So they had to get the letters translated. Even though Julie translated the very first letter, suddenly they had to have someone at the University translate them. Then all the vets (Bo and Hope, Doug and Julie, John and Marlena) spent the entire summer, sitting around "reading" the letters. That's it. No other story for them. Despite the fact that for years, the entire feud with Stefano involved all of them being kidnapped, brainwashed and tortured.
The letters were correspondence between Santo and Colleen. One incredibly stupid point however, is the fact that the correspondence amounted to Santo and Colleen going into vivid detail about events the other was present for (in some cases, was the only other person present) And since at the end of it, she was believed to have died, obviously the letters didn't come years later in retrospect.
It all started in Ireland (where the whole thing took place). Colleen was a young novice (a nun in training); she had yet to take her vows. Santo was a business man/trader from Italy and got caught in the middle of a bar brawl and was injured. He was taken to the church and Colleen was called upon for her medical training (....?). It was (apparently) love at first sight for them, after which the two kept finding excuses to see each other. Colleen was much more coy and reluctant to admit anything of the sort, since she was a novice and it would be improper; especially since Santo admitted had a wife and in fact had a young son, Stefano, roughly the same age as her brother Shawn. Stefano came with Santo and Santo had him play with Shawn, using the boys as an excuse to see Colleen and get her to see him outside the church. Santo was far more forward with his feelings towards Colleen, always pushing her to take things one more step (meeting without a chaperone, meeting without her wearing her novice habit, meeting without the pretense of the boys playing). At one point he told her his wife was dead, which Stefano would later reveal to Shawn not to be true; nor was it true that she was sick, which was what Santo told Colleen during one of their initial meetings.
Eventually Santo convinced Colleen to sleep with him and then proposed marriage. They were set to be married and spend their life in America; Colleen had even told the Priest at her church that she was leaving.
Shawn felt the need to stop her and told their father what Stefano told him about Santo's wife. Their "Da" found Colleen and Santo and he revealed that Santo's wife was still alive, devastating Colleen. She ran off and next we saw her, she was in a full habit, about to take her vows. Santo came to the church and stood at the back to watch. Colleen turned to see him and suddenly ran off. Later, they found her clothes at the edge of a cliff, which everyone assumed meant she threw herself off, even though they never found a body. Young Shawn became consumed with guilt, and vowed never to speak of this horrible orrurance every again. For this, Santo blamed 10-year-old Shawn and on his deathbed, asked his son to make Shawn and his family pay for his loss.
None of this really explains Stefano's actions over the years, especially the extent of the elaborate plots he's cooked up. He has yet to actually be responsible for a single Brady's death. He's even gone to the trouble of healing his supposed enemies when they're dying, seeing to their recovery and in case, genetically engineered a pair of super smart, "perfect specimen", fraternal twins that were Bradys! Nor does this explain the fact that he's been just about equally obsessed with the Hortons and all the family of friends of those two families, nor his penchant for brainwashing people.
But on the other hand, Hogan Sheffer's a hack, that couldn't write his way out of a paper bag, so we're lucky the story was even remotely coherent.