The details of definitions vary, but the following is a good catch-all:
An algorithm that provides high-level abstraction and modelling of data based on large training sets
This requires explanation in itself.
Abstraction implies that the outcome and input data are significantly different, the outcomes being, for example, image classification, predictive behaviour or even language translation. Abstraction means that there is not a simple relationship between input and output and in this case, it is most likely an unknown relationship, also known as a ‘black box’.
Modelling means that we are trying to create a real-world scenario of some kind so that a real-world classification or result is output.
The terms about data and large training sets imply that the data may be diverse and there is some variability in the input data. Usually, the ‘learning’ part of deep learning or machine learning means that the important features are detected as part of the learning process.