We would start by first defining a feature according to data science and machine learning, a Feature is an individual measurable property or characteristic of a data point that is used as input for a machine learning algorithm.
Feature Engineering on the other hand refers to the process of transforming raw data into features that are suitable foe machine learning Models. The success of machine learning models heavily depends on the quality of features used to train them.
To get into feature engineering one must be conversant with these five fields;

Feature Creation. This is the generation of new features based on domain knowledge. A deep understanding of the
intended field of application is required for effective
feature creation to ensure meeting of need and utility.
Knowledge on mathematical operations such as mean, mode,
median, sum, difference are essential.

Feature Transformation. This refers to the process of
transforming the feature into a more suitable
representation for the machine learning model. This is done through the application of techniques such as normalization, scaling and encoding

Feature Extraction. This refers to the creation of new features from existing ones. Done mostly to improve on the performance or diversify the utility of the feature.

Feature Selection. This is the selection of the subset of relevant features from the dataset to be used in amachine learning model. They are of several types, filter method, wrapper method and embedded method.

Feature Scaling. This refers to the process of transforming the feature so that they have a similar scale. The technique of feature scaling is sometimes reffered to as feature normalization. Commonly used processes include, min_max scaling and standardization/variance scaling.