In industry, what type of new data science algorithms does one develop? I've seen several job descriptions for data science which include developing a novel algorithm to be a part of production environments.
Can you give some input of what could be meant here exactly? Would they mean an algorithm that behaves somewhat of an ETL: getting the data, cleaning it, storing it, and running a known model on it? Or something more complex like building variations of known prediction algorithms? Some examples will really be nice, as I'm studying to go into this field.
I am no data scientist, only an aspiring one for two years, moving from my background in software engineering and mathematics. So I took some courses, had some interviews, read a lot on the subject online. My opinion:

New algorithms are developed in research centers and at universities. And even then, most algorithms used in companies are already developed, and just optimized even more.
Don't get your hopes up or be afraid that you have to reinvent gradient descent backpropagation.

With developing algorithms they most likely mean data extraction, data cleaning, data preparation for reporting statistics and presenting graphs. Maybe programmatically, maybe just using tooling.

The presented data may give more insights in simple relations in the domain, and maybe insights in more complex questions that can be asked. 

You may get to define data flows, get to compare and select machine learning algorithms and tune its parameters. And continuously evaluate model performance in practice.