What is covariance ?
If two ingredients both increase (decrease) at the same time, their covariance is positive. For example, less flour is required when the number of eggs is reduced. However, if two ingredients vary in opposite direction, their covariance is negative. For instance, less sugar is needed when honey is added to the recipe. Lastly, if two ingredients don’t have any effect on each other (i.e.: if they are independent), their covariance is zero.
Let’s continue with the baking analogy to explore another characteristic of covariance. If the covariance between eggs and sugar is 3 and the covariance between flour and cocoa powder is 10, can we conclude the latter covariance is stronger than the former? The answer is no. Covariance does not give us the strength of the relationship between two variables because it doesn’t have a minimum and a maximum value (i.e. it is not normalized). Its magnitude depends on the magnitude of the variables.
In probability and statistics, covariance is formally defined as “the expected product of deviations of two random variables from their mean values” (lab 551, lecture 3). In other words, it tells us whether we should expect one random variable to be below (above) its mean when the other is.
Covariance plays a key role in data science. Random variables with high covariance can be combined without losing significant information. It is also useful for inferences; it can be used to predict one result from another. In addition, it allows the integration of data from multiple sets which is key to machine learning.
Source:

Michael Gelbart. (2018). “Descriptive statistics and probability for data science, lecture 3”.https://github.ubc.ca/MDS201819/DSCI_551_statprobdsci_students/blob/master/lectures/lecture3.ipynb

“Statistics how to?”.Covariance in statistics: what is it?Example. Read on September 14, 2018 from http://www.statisticshowto.com/covariance/

Ruslana Dalinina. “Oracle+ Datascience.com”. Introduction to correlation. Read on September 14, 2018 from https://www.datascience.com/blog/introductiontocorrelationlearndatasciencetutorials

Brian Stacey.”Quora”. What is the purpose of covariance in statistics ? How does it differ from correlation? Read on September 14,2018 from https://www.quora.com/WhatisthepurposeofcovarianceinstatisticsHowdoesitdifferfromcorrelation

Brian Quanz.”Quora”. What are the applications of data science. Read on September 14, 2018 from https://www.quora.com/Whataretheapplicationsofcovariance

Alan Anderson “dummies”. How to measure the covariance and correlation of data samples. Read on September 14, 2018 https://www.dummies.com/education/math/businessstatistics/howtomeasurethecovarianceandcorrelationofdatasamples/

Stack exchange. What is covariance in plain language. Read on September 14, 2018 from https://stats.stackexchange.com/questions/29713/whatiscovarianceinplainlanguage