Roughly http://www.csun.edu/science/ref/pedagogy/active-passive/active-passive-learning.html gives the basic answers. Computational models follow these directions, that is in passive learning the learner answer only when is asked, (he might also say "I don't know" or give a wrong answer) while in active learning, the learner can ask questions to direct the learning process.
One of the best introductions to active learning is
Settles, B. Active learning literature survey. University of Wisconsin Madison., 2009
research.cs.wisc.edu/techreports/2009/TR1648.pdf
also note that, depending on conditions, active learning can perform worse than simple approaches to instance selection, such as guided learning:
Attenberg, J. & Provost, F. Why label when you can search?: alternatives to active learning for applying human resources to build classification models under extreme class imbalance Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining, ACM, 2010, 423-432
http://dl.acm.org/citation.cfm?doid=1835804.1835859
Put simply, active learning involves interacting with the environment (the world) without knowing the consequences beforehand, so for example, in computer games you put rules of the game and the learner tries these rules over many iterations while assessing a sequence of moves (in the medium and long terms) on the final outcome (winning the game) .. Car racing is a good example ...
Currently, most of the adaptive systems are built upon active or passive learning approaches. In active learning approach, the learning model is updated based upon the detected shift in the data stream using a change or shift detection test. In passive learning approach, the learning system is updated continuously, assuming that the environment is constantly shifting. It does not requires any shift detection test.
Active learning is about being proactive to a problem. For example, research is a proactive phenomenon. You seek information about how nature works, remember, we do not make laws of nature. Newton, or Einstein, Faraday and all other numerous scientists observed nature to discover how it works. So they tried to arrange for some experiments and learned that despite all efforts of a 'controlled' environment, they failed to equate the theoretical answer with a practical answer. Hence they suggested 'alpha, beta, gamma, etc as a digit by which the practical answer will come too close to theoretical answer, hence the term 'empirical formulae' . On the other hand, passive learning is as it comes to you, for example, you go to a class and you are taught something, you never had a plan to learn that but the teacher taught you maths, or physics etc.
Active learning is about being going after some problem with an approach to solve it.
I hope this clarifies the difference.
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