I cannot find the general definition of what is a classifier? I understand how it can work, but I can't come to a definition.
"An algorithm that implements classification, especially in a concrete implementation, is known as a classifier. The term "classifier" sometimes also refers to the mathematical function, implemented by a classification algorithm, that maps input data to a category."
For the whole source: http://en.wikipedia.org/wiki/Statistical_classification
A classifier can also refer to the field in the dataset which is the dependent variable of a statistical model.
For example, in a churn model which predicts if a customer is at-risk of cancelling his/her subscription, the classifier may be a binary 0/1 flag variable in the historical analytical dataset, off of which the model was developed, which signals if the record has churned (1) or not churned (0).
A classifier is a system where you input data and then obtain outputs related to the grouping (i.e.: classification) in which those inputs belong to.
As an example, a common dataset to test classifiers with is the iris dataset. The data that gets input to the classifier contains four measurements related to some flowers' physical dimensions. The job of the classifier then is to output the correct flower type for every input.