"Responsibilities" are individual items of work that you are supposed to do. For example, if you work at a restaurant and part of your job is to sweep the floor every day, sweeping the floor is one "responsibility".
"Delegating" responsibilities means getting other people to do them for you. While that might sound lazy and irresponsible, the word "delegate" actually carries a positive meaning. In the U.S., people think that delegating responsibilities is one of the most important skills that a good manager must have.
In addition to "responsibilities", here are some other words that work well with the verb "delegate":
- delegate work to someone
- delegate responsibility (This is different from "responsibilities", which are individual small jobs. "Responsibility" is the overall amount of things that you are in charge of.)
- delegate a task to someone