Product keywords are the words and phrases that people type into search engines in order to find what product they're looking for. By extension, they also describe what a piece of content (or an entire website!) is all about, and they're the words at the heart of on-page optimization. They still play an important role in a site's ability to rank, so by identifying the right words and phrases to target you can have an outsized impact on achieving your SEO goals.
The importance of product keywords: Product keywords are important because they are the linchpin between what people are searching for and what you are providing to fill that need. Your goal in ranking on search engines is to drive organic traffic to your product from the search engine result pages (SERPs), and the product keywords you choose to target (meaning, among other things, the ones you choose to include in your content) will determine what kind of traffic you get. If you own a golf shop, for example, you might want to rank for "new clubs" — but if you're not careful, you might end up attracting traffic that's interested in finding a new place to dance after dark.
Keywords are as much about your audience as they are about your content because you might describe what you offer in a slightly different way than some people ask for it.
Google recommends long-tail product keywords: Long-tail product keywords are those three and four keyword phrases that are very, very specific to whatever you are selling. You see, whenever a customer uses a highly specific search phrase, they tend to be looking for exactly what they are actually going to buy.