How would you explain first party data to a client?

I say it's the information people give you directly: email signups, purchases, what they do on your own site and app, form answers. As opposed to third party data, which is bought or tracked across other people's sites, and is getting harder to use as browsers and privacy rules clamp down. Does it matter small? Yes, mainly because an email list and your own analytics are things nobody can take away from you. You don't need a data platform, just collect it properly and with consent.