Forced into a position or situation where, under normal circumstances, wouldn't have fit or belonged otherwise.
Much like the device the term was named after, it is awkwardly insisting something to be where it shouldn't.
The producer insisted the writers shoe horned a romantic sub-plot in what was supposed to just be a horror-themed crime drama.
"There was no opportunity in the conversation for Chris to talk about this thing that was only interesting to him, so he shoe-horned it into the conversation with an awkward segway."
Verb | The act of 'slipping' something, such as an idea, political argument, or theory/concept into a conversation where it does not really fit; like using a shoehorn / shoe-horn to slip a foot into a tight-fitting shoe
"We were talking about the upcoming music festival when all of a sudden Harry and Arnold entered the conversation, continuously shoe-horning trump and politics