(Sorry for the long reply!)
Thanks everyone for your replies so far - it's so useful to hear lots of different viewpoints from people who've been involved in school governance.
One of the reasons why I'm so interested in being a governor is that it seems (to me anyway) to be a very worthwhile way of contributing to a school in a positive way and making a difference.
As I mentioned very briefly in my OP, I did start a teacher training course which I left due to lots of different reasons. I'm now working as a tutor, which I find hugely rewarding, as well as looking for more permanent full-time work.
As I am job-hunting right now, I have a lot of time that I would be able to give a school if I become a governor, as well as energy and enthusiasm.
To summarise my motivation for considering school governance, it would be a hope that I would make a positive difference to the school as well as feeling that I could bring a variety of skills to the role: communications and editing experience (I could write newsletters or take minutes, for example), knowledge of languages (French and Spanish) and teamwork experience.
I am also fairly young (25) and left education relatively recently, which would again bring a different perspective and viewpoint to a governing body if, for example, the other members of the body are either retired or currently employed with many years of experience in their professional field.
I am also looking forward to potential opportunities for personal development that may present themselves in the role. I read a couple of articles in the Guardian about young people becoming governors, and a lot of them talked about what a worthwhile role it can be, both in terms of helping others and furthering their own learning and skills.
Now to address some of the drawbacks that people have mentioned. I'm really grateful that you have pointed these out - thank you.
Again I understand that the school in which governors are placed will have an effect on their stress levels and level of responsibility, as well as whether they feel that they are making a difference or not.
I understand fully from what many of you have pointed out that the role comes with a lot of responsibilities, and is very demanding. In terms of the huge amount of paperwork that governors often have to deal with, for example, I feel that I would be able to deal with this at the moment, particularly as I have a lot of free time due to freelance tutoring commitments.
Does anyone have any advice please on how to cope with particularly heavy amounts of paperwork or any stress that might come with the role?