When the Italian word espressivo appears in a piece of sheet music, it means that the singers or instrumentalists should perform the marked passage of music with extra feeling.
You may have seen movies where characters try out for a musical role. Some of them sing not quite in tune. Others get all the notes right, but are boring to listen to because no emotion or feeling comes through in their singing. They aren't singing espressivo! In such movies, the hero or heroine gets the role because the director listening to them is moved to tears or excitement by their espressivo singing.