The Kronstadt affair or the Kronstadt rebellion was a series of demonstrations against the Bolshevik government. It was important because it was the first huge demonstration against the government after they'd established themselves. Also, it was by the military who the government had always relied on support from because of Lenin's April Thesis (1917, outlined the aims of the B. party and amongst other things eliminated rank). Oh, and the Communists hated opposition to their rule.
The military protested 'cause they saw the government as weak at that particular moment, after fighting between Trotsky and Lenin over the role of trade unions. They called for "Soviets free from Communists". By this saying this, they wanted a return to a government structure prior to the Bolshevik concentration of power and the creation of the Sovnarkom. - this was important as the Soviets at that time, which were still democratic, were not controlled by the Bolsheviks; they only controlled the policy-making body (can't think of the name =P)
Trotsky suppressed the rebellion by get the Red Guard to kill 15,000 soldiers and sailors.
That help?