To summarise the different components of Data Science, i think the following diagram does a very good job.
Interestingly this uses a mathematical visualization, the Venn Diagram to explain. Over the years there have been a number of variations on this, but i personally think this is one of the better ones.
Domain Expertise :- This is typically your business knowledge and understanding.
Mathematics :- Such topics as probability, statistical modelling, linear regression.
Computer Science :- Programming knowhow and expertise, as well as having the right architecture/infrastructure to store your data.
The Venn diagram, also shows the cross overs of each area, with the middle section (all 3 areas) forming “Data Science”. Anyone with expertise in all 3, are often termed “Unicorns”, a rare breed in the Data Science world.