It totally depends on the type of project they are working on but mainly they are responsible for testing the software. But if we generalize it then a Selenium developer has to do the following tasks on a day to day basis:-
Selenium testers have to analyze the business requirements for determining the test strategy which will be covered by automation testing.
They are also responsible for developing new software test scripts.
They are required to maintain existing test scripts suites.
If they are senior tester then they are responsible for helping Selenium testers.
If you want to become a Selenium developer then you must take-up the following Selenium training course. You can also watch the following Selenium video tutorial to learn more about it.