If you want to know the meaning of your words, look at your partner. Their reaction defines the meaning.
Beautiful, isn't it? And so true. If your character says something along the lines of "Stephan, I'm divorcing from your sister", you might think it holds a lot of meaning. But this is totally out of your hands, as it's the character Stephan's reaction to your words that instills (or detracts) any meaning to them.
On the other hand, if your character has a line "Do you want some coffee?" and your scene partner turns silent and looks at you angrily, all of a sudden this inconspicuous sentence appears to imply a lot of shared history and thus meaning.
Another great example of how in improv the responsibility of a scene or story can never lie with one person. Improv is always working together at heart.