WooCommerce is an open-source ecommerce platform for WordPress. You install it as a plugin on a WordPress website and use it to add a shop: products, stock, basket, orders and payments. WooCommerce describes the core platform as free. Because it runs inside WordPress, your shop and the rest of your website share one system.
How does it differ from Shopify?
With WooCommerce, the shop runs on your own WordPress installation, with a hosting provider of your choice. That gives you a lot of freedom in theme, plugins and code, but you also handle updates, hosting and security yourself. With Shopify, the platform takes care of that technology. Which option suits you depends on your range, your team and your budget.
What should you watch for in SEO?
A lot depends on the theme and the plugins. They determine, for example, the titles, the canonicals, the structured data for products and how faceted navigation ends up in URLs.
Example
Say an online shop for garden tools installs a filter plugin. Every combination of brand, price and material gets its own URL. Without clear choices about which filters may be findable, the number of addresses grows quickly.
Common mistake
Running two plugins side by side that do the same job, such as two SEO plugins or two plugins for product schema. The HTML then contains duplicate or conflicting data.
Outseen has a standard approach for online shops on WooCommerce. Key settings and pitfalls are covered in WooCommerce SEO: key settings and pitfalls.