Jimmy Speckerman is a character that was introduced in the episode "The Speckerman Recurrence". Jimmy was one of the people (other than his sister) who bullied Leonard in high school. He is portrayed by Lance Barber, who later portrays Sheldon's father in Young Sheldon.
In the episode, Jimmy contacts Leonard through Facebook, telling him he wants to meet for a drink. Leonard struggles to decide whether to meet him, but decides to do it, and "say all the things he wanted to say in high school".
At the bar, Jimmy greets Leonard like an old friend, much to his surprise. He then gleefully recounts their high school days, completely oblivious to the discomfort he is causing Leonard. After ordering a beer, Jimmy proceeds to ask Leonard for help designing glasses that show non-3D movies in 3D, mentioning that he needed Leonard's help, because he was "the smartest person" he could think of.
Sheldon stands up for Leonard and tells Jimmy he should apologize for all the heinous acts he committed against Leonard as a teenager. They show him a list of all that he did to Leonard. Jimmy says that he thought they were only having some fun, where Leonard counters that it wasn't fun for him, and they leave.
A drunk Jimmy later shows up at Leonard's apartment, along with the list, and starts to apologize for all the things he did to him in the past. Leonard does not want him driving drunk, and takes him in for the night.
The next morning, Jimmy wakes up with no re-collection of apologizing to Leonard. When he is reminded of it, he chides Leonard for having held a grudge and yet again calls him "Nancy".(likely indicating that Jimmy only apologized because he was drunk and has no memory of doing it.) Taking a stand, Leonard tells Jimmy to get out and actually shoves against him, not doing any damage. The guys are then seen running down the stairs to evade a very angry Jimmy.