My adviser is chairing a conference, as a PhD student how can I benefit from that

Help with organizing is a great start. Do what needs to be done and don't let any task be "too low". Top volunteering spots are registration help and IT support. You can build quite a bit of good rapport by being "so and so's friendly phd student who helped get my mac to connect to the projector". Makes your adviser look good as well. Happy adviser, happy phd life.

As someone who was in your position working with a faculty member who was an executive director of a conference, I did the following-

1. helped with registration
2. took photos
3. helped with general tech support issues
4. passed out drink tickets
5. whatever little thing needed to be done

In short, there is a TON to do behind the scenes at a conference to make things tick. Just be a can-do and helpful person. People notice that and it has the ability to do much more for your career than reviewing a few proposals. Those people you are helping get their mac to work on a projector might be on a search committee for a position you are applying for.

TL;DR: you can benefit in a small way by helping out with organizational duties, if you don’t let it distract you from more important work. Also, do not expect to review paper submissions - that is not typically something that PhD students are assigned to do.

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Organizing a conference is mostly an exercise in logistics, and involves taking care of many small and (usually) not very interesting details. It is quite common that faculty members who are organizing a conference outsource some of the organizational duties to their PhD (and/or undergrad) students. I beieve that sometimes the students are paid for this.

As for your question, I think your advisor would probably appreciate if you simply asked them what are some ways you can help, and predict that they would be happy assigning you some organizational duties, but not to review papers, which is the work of the program committee that is typically made up of senior academics with established reputations.

Whether you “can benefit” from performing such organizational duties is not obvious to me. Some ways in which you might benefit are:

• You might get paid.
• You will get to share in the excitement of being part of the workings of an academic conference (perhaps with well known speakers or important people in your field).
• You might get to email or otherwise interact with such people as part of your organizational duties. As a result, they are marginally more likely to remember your existence if and when they encounter your name in the future.
• You will learn about how academic conferences work and gain experience in organizational activities, which you can list on your CV.
• Your adviser will be happy with you.

And here are some reasons why doing this might not benefit you (at least, not as much as you think):

• You likely will not get paid.
• The time you will spend helping out with the organization has an opportunity cost - you could have been using it for working on your research or doing other productive work that may be more beneficial.
• With regards to the perceived benefit of interacting with senior researchers (as mentioned above), in my opinion the correlation of this “benefit” to actual future career success is very close to 0. Unlike what @JWH2006’s answer suggests, no one would be more likely to offer you a job because you did an especially nice job emailing them about hotel reimbursements, connecting their Mac to a projector, or handling some similar logistical issue. If you want to impress researchers in your area, talking to them about research during a coffee break at the conference would be hugely more effective (assuming that you are actually an interesting person to talk to).
• I think there is also a psychological opportunity cost, namely the effect that by having the mindset of “how can I benefit” in connection with something that is ultimately a mundane event that has little connection to the actual research activities that a PhD student is expected to focus on, you will be at risk of being distracted from those more important goals.

Summary. Ultimately, while I think it could be fun and mildly beneficial for you to get involved in the conference organization, it would be good not to get too hung up on the idea of using this as an opportunity for career advancement.

I was part of organizing committee as a first year PhD student (not in USA; we start PhD after completing master studies). I checked for locations for the icebreaker event, figured out transportation to there, accepted registrations and generally participated in planning and implementing other practical things.

The conference is an annual one and a significant in my field and my country, so one consequence is that many people recognized me after the event, even though I had little idea of who they were.

This also gave me experience, and, more importantly, confidence, in organizing things, which has been useful in my personal life.

I can't say if there have been any, or any direct, academic benefits. I am presently a postdoc of a person who attended that conference, and who is not from the country in which the conference was organized.