Recently, my sister (a long-time assistant) retired. We were doing some work together and because she knew how busy I was at my day job, she immediately took over and started to do the small tasks she knew I didn't have time to do. I appreciated all over again how nice it can be to have an assistant, and not only an assistant, but a very experienced one. I didn't have to worry about a thing because I knew she was taking care of it. It took a real burden off my shoulders. Unfortunately, this arrangement will be short lived, but it did remind me again how important our role can be.
I have also seen what it is like when it doesn't work. If a boss and their admin are not communicating expectations, that can create more work for both of them. It is important that you both know what the other does and where the assistant can take over and the boss can leave it. This way it can work beautifully.
For instance, I have a flagging system with my boss for her emails. If I have handled it, I put a checkmark so she knows I have done whatever I need to do and she can just read it for information knowing it is being taken care of. If it is an item she needs to read, I flag it for her and wait to see what her instructions will be. She usually cc's me on the email when she replies and then I get to work on whatever it is she wants me to do.
This system has been working well, but it took awhile for her to catch on. At first she was replying to a lot of the emails I had already handled. Thankfully, we were saying the same thing, but I needed to reiterate a few times that I was handling it. I think she finally got it because the last time I was in her office, she mentioned she saw the checkmark beside it so knew I was handling it. It sometimes takes awhile for your boss to really have trust that the work is being taken care of and will be done, but if you are consistent, over time they will see you are on it.
It also depends on your boss. My previous boss had no problem handing over things to me and expected I would have the work done. I don't think it ever crossed his mind I wouldn't do it. His expectation actually helped me to be focused when going through his emails to ensure I handled whatever I needed to. Having a one-on-one meeting afterwards, was always a good way I could catch him up on the things I had done and where we were at. Communication and consistency are key. As your boss gets used to the new working arrangement, things will go smoother.
I also find we have a role to play to help our bosses have more confidence that the job will be handled appropriately. If my boss asks me to do something, I write it down as she is telling me. She can see that I am writing it down and that helps her to have confidence that it won't be forgotten. Sometimes I will repeat it back to her to satisfy myself that I have it right, but also to help her to know I have it right. If there is a misunderstanding, that will be a good time to clear it up and get on the same page.
I also ask questions if I don't fully understand what she wants me to do. Don't say you understand, if you don't. Sometimes you may think you understand, but when you get back to your desk and start the task, you have more questions. Never be afraid to ask questions. This will also give them confidence that you understand the task. Of course, it is always good to go into a meeting with all your questions in one meeting rather than asking here and there, but at times you need to ask to make sure you are doing what is required.
When the assistant/boss relationship is working, it can be great!