I have this title in my company. Inside our firm they call me a PM but on my business card it says: Project Manager/Analyst
I am curious, what exactly does Manager/Analyst mean?
I don't know if that's the best way to say but, titles means almost nothing nowadays. That's not myself stating it. Take a look at THIS article, for instance.
It is important - and I believe that's what you're trying to do - to understand what are your roles within the company. So, based on it, I'd go for angeline's (+1!) answer:
Your company - that gave you the title - is the only one able to clarify you your roles.
There's a very goood article on INC that states 8 qualities of remarkable employees. Take a look at number one.
Understand and enjoy your new role, in despite of the title it has.
The card means that you have two roles:
You are responsible both for managing a project or projects, and for helping the business to analyze what they're doing and what they should do next.
The word "Project" is almost certainly associated with "Manager" rather than with "Analyst", so read it as (Project Manager)/(Analyst) and it might make more sense.
Of course, if you don't think that these two roles are what you're actually doing, you might want to discuss that with someone.
The only answers you can get here will be generic, because Project Managers and Analysts terms can represent different levels of roles and responsibilities from one organisation to another. If you want to know exactly what this means, talk to your manager to get some clarity as to what this combined title entails in your organisation.