I have just moved into Product Marketing from Customer Retention. My questions are, 1) what is the core job of a product marketer, and 2) what skills do I need to work on?

There’s an awesome blog post that I’d highly recommend written by Dave Gerhardt (super impressive marketer who produces a lot of solid, thoughtful content) for your question what does product marketing do and what are we responsible for: https://www.drift.com/blog/what-is-product-marketing/. For your second question on what skills you need to work on, that of course depends on where you’re already strong vs where you have opportunity to improve, but generally I would say a great product marketer is able to:

• Understand and empathize with your customer/buyer
• Create compelling messaging and positioning
• Understand, pitch, and demo your company’s product(s) 
• Deliver strong, convincing presentations internally and externally
• Research industries or markets and find the opportunity for your company to pursue, plus recommend the value props they should use to differentiate
• Drive GTM workstreams and align stakeholders and influence them to action