Can someone help me answer this question about homeland security? Thank you!
Your first stop should be their website: https://www.dhs.gov.
Specifically, you should go to their Mission page, https://www.dhs.gov/mission. On it, it states: "Missions include preventing terrorism and enhancing security; managing our borders; administering immigration laws; securing cyberspace; and ensuring disaster resilience."
As for the second question, "Why do you think the work of the department is so complex," consider that it is the third largest cabinet department and that it combines the functions of 22 previously-existing agencies and uses information from military and civilian intelligence sources.