Othello, of course, sees love as someone caring for him, showing tenderness toward him, and being devoted entirely to him.  Desdemona represents these characteristics, and for the first time in his life, Othello puts aside some of his military attributes and becomes vulnerability.

Desdemona complements Othello's view of love because she is moved by his stories and scars and desires to care for him.  By supporting him, devoting her time to him, and being willing to follow him anywhere, she believes that she is demonstrating love.

Emilia, likewise, is driven by her version of love.  While Iago treats her condescendingly, she still longs for his approval.  Hence, her giving him Desdemona's handkerchief.  She sees love as winning someone's approval.

If these characters did not view love in the manner they do, then Iago would not have been able to easily manipulate them.  He knows the version of love that each character possesses and uses it against him or her.