This is a really interesting question, Brad. There's not a simple answer to it because you are referring to song lyrics and they can often be full of phrases that don't really make sense, or are simply used because of the way they sound. However, I think that "strong" is a word that is growing in popularity for a number of different reasons. The traditional meaning of strong (when speaking about a person) would probably refer to physical strength. Nowadays, I feel that some men may call women "strong" because they are trying to accept that strength can be found in ways other than physical. I have my own opinion about why some men choose to call women strong, but that's mostly based on how I feel about people like Bruno Mars and Ed Sheeran ;) In conclusion, I think that your idea about this word is correct. They are referring to mental strength and independence. It is doubtful that those singers are singing about the physical strength of a woman that they loved, as generally speaking it isn't culturally desired for men to have a female partner that is physically stronger than them. Very short version: Call a woman strong if she beats you in a wrestling match, or has had many difficult moments/situations in her life to deal with.