Exploratory testing is like a chess game with a computer. Tester revise his plans after seeing the move of your opponent. Yet all your plans can be changed after one unpredictable move of your opponent. Can you write a detail plan for a chess game with a computer?
Player uses all his knowledge and experience. He can define only the fist move in the game and it is unreasonable to plan far ahead. You can plan 1 move ahead, or 20 moves if you're a very experienced player, but you can't plan the whole game. To plan 20 moves he had to spend a lot of his valuable time (the clock is ticking).
Of course he is trying to find some information about existing situations between moves. This is exactly what an experienced exploratory tester does.
After running any test case, testers may need to find additional information about application and system from a developer, system architect, business analyst, or may be from literature. A lot of information is necessary for correct exploratory testing. Other teams whose products are used for creating the applications have influence on our testing too.