In order to understand what happened, you need to understand a little bit about legislative procedure in the House of Representatives. Most legislation, in order to come up for a debate and vote, will pass through the Rules Committee after it leaves the committee of jurisdiction. The Rules Committee reports what's called, appropriately, a rule. A rule specifies the conditions and length of debate as well as if the bill may be amended. In short, it is a tremendously powerful committee which controls the flow of legislation through the House.

I won't spend as much time about the powers of the Speaker. As the presiding officer of the chamber, the Speaker controls debate by ruling on matters of procedure and choosing who to recognize (though this power is usually delegated). The Speaker also assigns bills to committees, appoints members to select and conference committees, and has a large degree of influence over assignment to standing committees through the steering committee.

The Speaker also appoints his party's members of the Rules Committee. Speaker Cannon went one step farther. He was a member and Chairman of the Rules Committee. In effect, this meant that he had autocratic control of the House. Cannon was generally opposed to the progressive faction of his own Republican Party and used his power to stymie their legislative activity. This went double for the opposition Democrats.

The "revolt" involved a group of insurgent Republican members joining with the Democratic minority to pass a reform of the House rules over Speaker Cannon's objections. The reforms, among other things, stripped the Speaker of the ability to sit on the Rules Committee. The tactics used to get the resolution to the floor were rather clever. One of the insurgents introduced it as privileged (thereby superseding other items on the agenda) based on a procedural ruling Cannon himself had recently made. The House overrode Cannon's hypocritical objection and then passed a modified reform. Cannon remained Speaker and, indeed, demanded what was essentially a vote of confidence, but was significantly weakened. The article you linked implies that Cannon was removed from the Speakership. He was removed in 1911, but that's because the GOP lost 56 seats in the 1910 midterms and Democrats took control of the chamber.

For what it's worth, the Speaker of the New York State Legislature also sits on and chairs that body's Committee on Rules. Fun stuff.