The short answer
First-party data is information a business collects directly, with the audience's knowledge and consent: an email address, a purchase history, a survey response. It stands in contrast to data borrowed through a third-party platform whose access and rules a business does not control.
Why it matters more as platform rules keep shifting
A social media following exists entirely under a platform's own rules, reachable only through an algorithm that can change at any time. First-party data, like an email list built from that following, is a channel a business owns and controls, independent of any single platform's policies.
Social media is often the acquisition channel, not the storage
A practical way to think about the relationship: social media is frequently where a relationship with a new audience member starts, while first-party data, an email list or a customer account, is where that relationship is retained and owned over the long term.