Othello's emotional journey is his change from a strong, resilient and determined military leader to a misguided murderer, carried along by the effects of of love, jealousy and ignorance.
He moves from the civility of Venice to the isolation of Cyprus as a physical journey, which also serves as a metaphor for his removal from polite society to vulnerability after his social transgression of eloping with Desdemona. Othello was only on the fringes of acceptability in Venice due to his military prowess,but this is not enough to sustain him in Cyprus, particularly after the Turks are no longer a threat.
Othello also journeys from being a man of strong will and self control to a figure overcome with passion and a loss of all senses. He may regain his composure at the end to attempt to draw back some of his noble spirit, but taking his own life - another journey of course - does not sufficiently avenge the others who have died in the course of the play.
Othello's journey could be said to be the reverse of the hero's journey. As the play begins, he has everything: he is the new general of the Venetian troops; he is newly married to the daughter of an important citizen; he is a strong, confident warrior. By the play's end, he has lost everything due to his belief in Iago's honesty. His physical health deteriorates along with his sanity as he becomes more tangled in Iago's web of lies. He suffers from seizures; he cannot sleep; he is constantly in a state of agitation; he becomes paranoid. His breakdown, of course, leads to Cassio's demotion and Desdemona's murder. This, in turn, leads to Emilia's murder and Othello's own suicide.
Physically, his journey took him from Venice to Cypress. While at the time Venice was considered a city concerned with vice (lust, greed, gluttony) it is also representative of Elizabethan England. Much of Shakespeare's plays were set outside England in order to disguise the many social critiques within them.
Emotionally, Othello finds that the insecurities revealed in the beginning of the play, (the revelation of his courtship with Desdemona to the Duke) eventually rear themselves as jealousy. It could be argued that his racial insecurities allow Iago's manipulation to infiltrate his psyche with consequence that he deteriorates from security and social acceptance, both as a General and as a Husband, into the savagery that was typecast upon him as a moor.