Uptime monitoring lets you know that your API is online, and available for your clients to reach (whether you're using your API to serve data to a frontend, or operating an API-first business such as Stripe or Twilio)
Good monitoring solutions let you know if there's an issue with accessibility in a much more understandable manner than others (Such as, 'Your API server is unreachable!' vs 'Could not make a HTTP connection to ...'), and notify you via Slack, Text message, or PagerDuty notification.
Why should you care?
Having a Slack notification when your API becomes unreachable is much better than an email from a customer!