The dominant symbol in Othello is the handkerchief, spotted with strawberries, Othello's first gift to Desdemona. It's white background is symbolic of Desdemona's suspected reputation (virginity), and the spots of red strawberries are indicative of the stains on her reputation as well as the blood that follows in Act V. Like the bed, another major symbol, it is first intended as a symbol of eros (physical love), but it is subverted and turned into a symbol of theros (death).
It is a symbol of either Othello's love for or possession of Desdemona. Othello, a former pagan,who sees the handkerchief as magical ("there's magic in the web of it"), and he speaks of it in mythological terms:
Did an Egyptian to my mother give;
She was a charmer, and could almost read
The thoughts of people: she told her, while
she kept it,
'Twould make her amiable and subdue my father
Entirely to her love, but if she lost it
Or made gift of it, my father's eye
Should hold her loathed and his spirits should hunt
After new fancies: she, dying, gave it me;
And bid me, when my fate would have me wive,
To give it her. I did so: and take heed on't;
Make it a darling like your precious eye;
To lose't or give't away were such perdition
As nothing else could match.
Notice that it is connected to the eye ("my father's eye" and "your [Dedemona] precious eye"), love ("subdue my father entirely to her love"), and supernatural spirits ("spirits should hunt / After new fancies").
Desdemona, a Christian, obviously doesn't see any of these connections; rather, it is a curse and a mark of jealousy:
Over the course of the play, the handkerchief is in the hand of nearly all the main players: it goes from Othello to Desdemona to Emilia to Iago to Cassio to Bianca. Notice, it goes from the top ranking male (Othello) to the lowest (Cassio, after he is dismissed), and it goes from the most reputable female (Desdemona) to a prostitute (Bianca). So, not only is it a dominant symbol of love and jealousy but also of gender and social class difference. Also, it is a means to achieve situational irony.
The handkerchief is important psychologically as well: did Othello set Desdemona and the marriage up to fail by giving it to her? Why does Emilia, faithful to her mistress, steal it and give it to her misogynistic husband?
All in all, the handkerchief is symbolic of the sexist double standards of the patriarchal society in which men control women: they are possessions to men. Just as Emilia says, "They are all but stomachs and we but food," so too it is with the handkerchief: men use handkerchiefs as possessions, play-things, as means-to-an-end, and, when finished, they dispose of them after having first blown their noses on them.