It's the bizarre practice of making a possessive out of the word "I" -- as in "Danny and I's relationship is stronger than ever."
Seriously? "I's"? You may be a famous actress or a TV personality, but you're certainly not smarter than a fifth grader!
It seems that a lot of people have trouble concocting a compound possessive -- a possessive involving more than one person or thing -- on the fly. And, I'll admit, it can be tricky.
One route is to avoid the issue altogether, saying instead something like "The relationship between Danny and me is stronger than ever." (But that brings up another bugaboo: the whole "I" versus "me" thing ... fodder for a future blog post.)
The easiest remedy, really, is to get into the habit of quickly breaking apart the compound possessive and letting your ear tell you what is right. Would you say, "I's relationship is stronger than ever?" Of course not. Your ear immediately tells you that the right word is "my." (Maybe an even faster way is to remember that “I’s” is never, never, NEVER right!)
Then do the same with the other noun in the phrase: "Danny's relationship is stronger than ever."
Glue the two parts back together, and – voilà -- you have a perfectly serviceable sentence: "Danny's and my relationship is stronger than ever." If saying it that way sounds strange, it’s because people just don’t get it right very often.
Here’s the deal: Don't be afraid of "my." It's a quiet but powerful little word that makes you sound very smart!