The Home Rule Crisis was a crisis over the issue of whether Ireland should be given home rule, in the shape of an autonomous Irish parliament. It started when a home rule bill was passed in 1912 and ended when the bill was suspended in 1914 because of the start of WWI.
The basic problem was that there were two parts of Ireland with different majorities. In Ulster in the north, there was a majority of Protestants who wanted to remain united with England. In the south, there was a majority of Catholics who wanted home rule. In each region, moreover, there were large enough minorities of the other religion/party to make any solution difficult.
In the crisis, the home rule bill was passed (it needed to be passed three times in successive years because of British law), leading to threats of rebellion among various factions. These threats and the worries they brought were the basis of the Home Rule Crisis.