It is not possible (at the moment) to make an artificial brain, but it is possible to make simplified artificial neurons and artificial neural networks. These ANNs can be made in many different ways and can try to mimic the brain in many different ways.
ANNs are not intelligent, but they are good for recognizing patterns and making simple rules for complex problems. They also have excellent training capabilities which is why they are often used in artificial intelligence research.
ANNs are good at generalizing from a set of training data. E.g. this means an ANN given data about a set of animals connected to a fact telling if they are mammals or not, is able to predict whether an animal outside the original set is a mammal from its data. This is a very desirable feature of ANNs, because you do not need to know the characteristics defining a mammal, the ANN will find out by itself.