In short, deep learning algorithms are mostly a set of ANNs that can make better representations of large-scale datasets, in order to build models that learn these representations very extensively. Nowadays it's not limited to ANNs, but there have been really many theoretical advances and software and hardware improvements that were necessary for us to get to this day. In this regard, Ian Goodfellow et al. (Deep Learning, MIT Press, 2016) defined deep learning as follows:
"Deep learning is a particular kind of machine learning that achieves great power and flexibility by learning to represent the world as a nested hierarchy of concepts, with each concept defined in relation to simpler concepts, and more ...
