Learn Russian: Вчера мы засиделись в кафе с обоими друзьями. - Yesterday we stayed up late at the cafe with both friends.

In Russian, wrapping a verb in the prefix за- and postfix -ся often shows that the subject got completely absorbed in the action, doing it to excess or losing track of time. While сидеть just means to sit, засидеться implies sitting around for way too long. Here, засиделись translates as stayed up late or stayed too long.

Why is the word for both spelled обоими here?

It is in the instrumental case because it follows the preposition с (with). The dictionary form is оба (both). When declining masculine and neuter nouns in the instrumental case, оба becomes обоими.

Wait, doesn't both also have a feminine form? Why isn't it used here?

Yes, the feminine form is обе. Because друг (friend) is masculine, we must use the masculine form оба and its declensions. If they were female friends (подруги), you would use the feminine instrumental form and say с обеими подругами.

Why does the plural of friend look a bit strange in с друзьями?