The white hat has to do with data and information. It is used to think or talk about facts, figures and other objective information. You're putting aside proposals and arguments and focusing directly on the information. You examine what information is available, what information is needed, and how it might be obtained. To remember the meaning of the white hat, think of a white paper which is neutral and carries information, or think of a scientists white lab coat.
The red hat has to do with feelings, intuition, hunches and emotions. It is the stuff you feel, but which you might not have any rational basis for. That might mean you're expressing your emotions and reactions, or it might mean you're expressing an intuition that you can't otherwise back up. The red hat gives you permission to put these things forward without having to need to explain them or justify them. You're speaking from your gut, and expressing what you really feel, rather than what makes sense. In a "serious" meeting, you're often not supposed to express your emotions, so people do it by disguising them as logic. The red hat allows you to express what you feel without having to call it anything else. Thus others won't have so much need for arguing with you about what you're saying. Think of red as fire and warm, or as a red heart.
The black hat is about caution and critical judgement. You bring up all the reasons why something might not work, the possible downsides, risks and worst-case scenarios. You're playing the devil's advocate, essentially, and bringing up logical negative arguments. This might allow us to avoid making mistakes and doing silly things that won't work or that will be illegal. The point is not just to be negative, but to address the possible problems that aren't being looked at. The black hat can be very useful in making ideas more practical, but can also easily be over-used to kill creative ideas. To remember the black hat, think of a judge robed in black.
The yellow hat is for optimism and the positive view of things. It looks for how something can be done, how it is feasible, how it is beneficial. When wearing the yellow hat one looks for opportunities, possibilities, potentials and positive benefits and outcomes. One examines the best possible outcomes. This is not just a general, abstract opimism, but it is looking specifically at the disirable benefits that might be available. You might find benefits in what otherwise seems like a negative situations. E.g. "A higher cost of energy might make everyone more energy efficient". Think of warming sunshine to remember the yellow hat.
The green hat is for creative thinking. One brings forth new ideas, additional alternatives, possibilities and hypotheses. You're provoking new thinking by bringing something new and unexpected into the picture, something that nobody might have noticed. You're examining how things might be done in a different way, how there might be different explanations to things than normally accepted. The green hat is brainstorming and coming up with fresh, innovative ideas. One is dreaming up ways of seeing things differently. The green hat isn't concerned with whether the ideas are practical, but is just throwing creative thoughts into the pot. Think of sprouting green vegetation.
The blue hat is about the overview and control of the whole process. A person wearing the blue hat will think about how the agenda is being carried out, and how the whole thing is working. It is a meta-perspective. "How is this going?", "Is this working for us?", "What are we learning from this?", "What would the next logical step be?". The blue hat asks for summaries, conclusions and decisions. It also can think about and comment on the thinking being used. It is reviewing things and, if necessary, trying to control the process. Think of the blue sky.