Several conflicts exist in the novel: wealth versus poverty, passion versus reasons, marrying for love versus marrying for security. The individual conflicts between characters exemplify these thematic conflicts.
There is conflict between Elinor and Marianne Dashwood. Elinor represents the sensible, reasonable nature, Marianne the romantic, passionate nature.
Marianne is in conflict with the Colonel Brandon who wants to marry her. However, she believes he is too old and sensible for her.
Marianne also has a conflict with John Willoughby with whom she is in passionate love but by whom she is later rejected.
Willougby also has a conflict with Elinor over the manner in which he rejects and hurts her sister. Later it is revealed that Willoughby must marry for money in order to secure his place in society, so he has not rejected Marianne for love but for financial reasons.
Elinor briefly allows herself to abandon reason and fall in love with Edward Ferrars. When she is rejected, she internalizes the conflict and chastizes herself for abandoning her sensibility. Edward, eventually, decides to follow his heart rather than his mother's wishes in finding an "appropriate" mate and returns to Elinor.