Regression and classification are both related to prediction, where regression predicts a value from a continuous set, whereas classification predicts the 'belonging' to the class.
both are the example of supervised learning.
eg : price of a house depending on the 'size' (sq. feet or whatever unit) and say 'location' of the house, can be some 'numerical value' (which can be continuous) : this relates to regression.
Similarly the prediction of price can be in words, viz., 'very costly', 'costly', 'affordable', 'cheap', and 'very cheap' : this relates to classification.
Each class may correspond to some range of values