The following answer is based on my understanding of what it means to organise a symposium in a conference (i.e., commonly a conference session of about 60 to 120 minutes with around 3 to 8 talks all with a common theme, where the chair is the one to invite and arrange the talks and often provides a more general introduction to the talks). Obviously, I'm not talking about the more mundane task of merely chairing a session, which can be as simple as you being the designated person that ensures that each talk keeps to time.
You can build relationships with the other presenters in your session. If you are organising a symposium, then you will be contacting other possible presenters who you think may be attending. This often provides an excuse to connect with people you may only know through their research. For people you already know well, it can provide an excuse to catch up at the conference, which in turn can flow into research collaborations or other opportunities.
You are likely to get more people to your session, and those that come may be more interested in your topic. If attendees see that your session is all about your topic, then people interested in your topic are more likely to attend. In contrast if you present an individual paper, it may get lost in a more general session.
Chairing a session can help people see you as a person active in the topic.
Chairing a session can be something you put down on your CV, performance review, promotion application, grant application, etc. It's generally not a huge thing. In many, but not all, fields, conferences are more a means to an end. In these cases journal articles and grants are more important. That said, chairing a symposium that you organised does show some academic leadership that would count for something.