1. Inception. This phase focuses on addressing business risk by having you drive to scope concurrence amongst your stakeholders. Most projects have a wide range of stakeholdres, and if they don't agree to the scope of the project and recognize that others have conflicting or higher priority needs you project risks getting mired in political infighting. In the Eclipse Way this is called the "Warm Up" iteration and in other agile processes "Iteration 0".  Disciplined Agile Delivery (DAD) also uses the term Inception phase.
2. Elaboration. The goal of this phase is to address technical risk by proving the architecture through code. You do this by building and end-to-end skeleton of your system which implements the highest-risk requirements. Some people will say that this approach isn't agile, that your stakeholders should by the only ones to prioritize requirements. Yes, I agree with that, but I also recognize that there are a wide range of stakeholders, including operations people and enterprise architects who are interested in the technical viability of your approach. I've also noticed that the high-risk requirements are often the high-business-value ones anyway, so you usually need to do very little reorganization of your requirements stack.  DAD has kept the Elaboration phase concept of proving the architecture, but instead of including an explicit phase for doing so it adopts the streamlined approach of doing so in the first iteration(s) of Construction.
3. Construction. This phase focuses on implementation risk, addressing it through the creation of working software each iteration. This phase is where you put the flesh onto the skeleton. DAD includes an explict Construction phase, and Scrum focuses on this.
4. Transition. The goal of this phase is to address deployment risk. There is usually a lot more to deploying software than simply copying a few files onto a server, as I indicated above. Deployment is often a complex and difficult task, one which you often need good guidance to succeed at.  DAD includes an explicit Transition phase.

Each phase ends with a milestone review, which could be as simple as a short meeting, where you meet with prime stakeholders who will make a "go/no-go" decision regarding your project. They should consider whether the project still makes sense, perhaps the situation has changed, and that you're addressing the project risks appropriately. This is important for "agile in the small" but also for "agile in the large" because at scale your risks are often much greater. Your prime stakeholders should also verify that you have in fact met the criteria for exiting the phase. For example, if you don't have an end-to-end working skeleton of your system then you're not ready to enter the Construction phase. Holding these sorts of milestone reviews improves your IT governance efforts by giving senior management valuable visibility at the level that they actually need: when you have dozens or hundreds of projects underway, you can't attend all of the daily stand up meetings of each team, nor do you even want to read summary status reports.

These milestone reviews enable you to lower project risk. Last Autumn I ran a survey via Dr. Dobb's Journal (www.ddj.com) which explore how people actually define success for IT projects and how successful we really were. We found that when people define success in their own terms that Agile has a 71% success rate compared with 63% for traditional approaches. Although it's nice to that Agile appears to be lower risk than traditional approaches, a 71% success rate still implies a 29% failure rate. The point is that it behooves us to actively monitor development projects to determine if they're on track, and if not either help them to get back on track or cancel them as soon as we possibly can. Hence the importance of occasional milestone reviews where you make go/no-go decisions. If you're interested in the details behind the project, they can be found at http://www.ambysoft.com/surveys/success2007.html .  More recent data can be found at ambysoft.com/surveys/ in general.

Done right, phases are critical to your project success, particularly at scale. Yes, the traditional community seems to have gone overboard with phase-based approaches, but that doesn't mean that we need to make the same mistakes. Let's keep the benefit without the cost of needless bureaucracy.