It's fair to say that Iago has a bit of a chip on his shoulder. A soldier from the lower-classes, he believes that he's been constantly passed over for promotion in favor of the likes of Othello and Cassio, despite the fact that he's proved himself in the field over many years. As such, Iago deeply resents these men and the society they represent, even though Othello, due to his skin color, is still regarded as something of an outsider.
In any case, Iago feels incredibly bitter and insecure. And it's no surprise that such bitterness and insecurity should plant the demon seed of jealousy into his mind and that he comes to believe that his wife Emilia is having an affair with the two men he hates most in all the world.
There's no evidence that the loyal and faithful Emilia is cheating on her husband. But for someone as bitter and as insecure as Iago, a little matter like evidence is completely unimportant; suspicions are all that he needs.
Regarding Othello, those suspicions surface in Iago's soliloquy in act 1, scene 3:
[I]t is thought abroad that 'twixt my sheets
He's done my office. I know not if 't be true,
But I, for mere suspicion in that kind,
Will do as if for surety. (I, iii, 324–327)
In other words, Iago's heard some rumors that Othello's been bedding his wife and although he doesn't know for certain if those rumors are true, mere suspicion is enough for him.
Iago expresses his suspicions of Othello in another soliloquy later on in the play, this time in act 2, scene 1:
For that I do suspect the lusty Moor
Hath leaped into my seat. (II, i, 220–21)
For good measure, Iago also expresses his suspicions of Cassio:
For I fear Cassio with my night-cape too. (II, i, 232)
In both cases, Iago's jealousy presents an additional reason for him to want to destroy these men. Already feeling resentful towards them for taking what he believes to be the promotion that is rightfully his, he can now use his unfounded suspicion that they are sleeping with his wife as a further justification for embarking upon his dastardly revenge plot.