In traditional programming, developers give computer explicit instructions in procedural top down scripts and or via control flow statements that can “jump around” as opposed to top-down. Machine learning and deep learning is about supplying well-known, proven algorithms with cleaned, feature selected and or feature engineered data, as well as corresponding labels for the data (in unsupervised learning, only data is supplied), the algorithm leverage loss calculation, metrics, and optimizer to update parameters such as weights and coefficients in the algorithm. Finally these learned weights and coefficients are used along with the algorithm for prediction.
The more high quality data the better.
The biggest difference is: developers give specific instructions in traditional programming, and in machine learning and deep learning algorithms learn parameters based on data and loss function rather than rules.
Not having to write all the rules has benefits especially when the rules are hard to encode or program. The final product is also more robust, less likely to fail because it is not a strict rule based program.
Deep learning uses many layers of neural networks, hence the word deep. It is usually consisted of weight-learning layers or neural networks. Neural networks stacked together, have the unique capability of being universal function approximation - representing complex functions without explicitly coding them.