Sense – (1) power to see, hear, taste, feel, etc. (2) sound judgment (3) meaning, substance (3) awareness (4) intelligence, ability to make intelligent choices and to reach intelligent conclusions or decisions (5) Eleanor Dashwood
Sensibility – (1) delicacy of feeling, (2) sensitivity (3) Marianne Dashwood
The title is significant because it represents two of the main protagonists in the story (not that there is/are any antagonist/s).
Eleanor, as the eldest sister in the Dashwood family, is more careful with her judgments, as well as in giving her opinions or in sharing secrets. She is able to step back and weigh things before making a move or decision. Not until the end, Eleanor was very discreet with her feelings for Edward Ferrars. She was willing to let things pass between her and Edward until she learns that he wasn't going to be married to Lucy Steele, with whom he was "engaged."
On the other hand, Marianne Dashwood is the more emotional sister. She is poetic and dramatic as depicted in the scene where she was talking to her mother, Mrs. Dashwood, about her fairy tale-thoughts on love. Mrs. Dashwood responded to Marianne saying something like, "You're taking your romantic sensibilities a little bit too far." Also, Marianne is the more temperamental of the Dashwood sisters. She is easily swept by emotions and her fantasies on finding love and happiness.
What makes the title more significant is that towards the end, Eleanor and Marianne's characters weren't restricted to being Sense and Sensibility, respectively. Eleanor finally warms up and breaks free from her emotions. Marianne had some "sense" knocked into her in finding the happiness that she longed for.
What makes Sense and Sensibility appealing is that it is reflective of life. It doesn't dwell on anything fictional and grand, but i