Data analysis is the practice of working with data to extract meaningful or useful information which can then be used to make informed decisions.

Let's take an example for more clarity. Let's say you work as a data analyst for a home automation company based on the previous year's data. You notice that there is this certain x product that has had its best sales month during October and November. Now looking at all this information, you are going to predict a similar behavior for the upcoming years as well,  which sounds pretty obvious now, right?

Data science, on the other hand, is an umbrella term that encompasses data analysis, data modeling, data mining, machine learning, and other similar disciplines.

Data science uses more sophisticated and complex machine learning algorithms to build predictive models. An example of that will be something that we use in our day-to-day. Any search engine like Google, Bing, or Yahoo, uses data science algorithms to come up with meaningful results for your search query within a fraction of a second.