Claudio has been deceived into thinking that Hero has been unfaithful to him by standing at a window at night and speaking to Boracchio. Boracchio had been speaking to the waiting gentlewoman Margaret, but had the intent to deceive Claudio. Claudio, who is in love with Hero and had every reason to believe that she has always been pure in word and action, was cruelly hurt by this and, by the standards of the day, had every right to repudiate his bride-to-be.
And repudiate her he does. He says, in a fit of anger, the most damning things about a woman in Hero's position. "She's but the sign and semblance of her honor./Behold like a maid she blushes here!... She knows the heat of a luxurious bed;/Her blush is guiltiness, not modesty." He refuses to marry her on the grounds that she is impure (which Hero refutes) and gives her back to her father Leonato. This incredibly dramatic scene becomes even more so when Hero swoons, and Claudio, Don Pedro, and Don John leave the scene not knowing if Hero is alive or dead.
Don John had engineered all this deception, purely, it seems, to cause trouble for Count Claudio and, by extension, his half-brother Don Pedro. Like other of Shakespeare's villains (Iago in Othello, for example), the illegitimate character has obscure motives for wanting bad things to happen to the legitimate characters. In this instance Don John seems to be causing trouble for others, because he believes doing so "blesses himself every way."