What are the differences between biased and unbiased learners?
Biased in the context that you are speaking means, that your model overfits the training data and can not generalize well. It means your model performs very well on your training data, but can not do well on cross-validation and test data. It is customary to say that biased learners memorize the training data which is really true. Biased learners don't learn the data, they fit the data. For understanding the other usages of bias take a look at this question.

There is something that may be worth mentioning. You may have heard people saying that your model has a high-bias problem. It just means that your model can not learn the training data, whilst the biased learners overfits the training data, means fits the training data. The latter can not generalize well because it has fitted the training data, memorized it, the former can not generalize because it has not learnt even the training data so it has not learnt so much and can not generalize.