Definition
SNI is defined in RFC 6066. Without it, every HTTPS site would need its own IP address. With it, the server knows which certificate to present before encryption begins.
How it works
The hostname is sent in the Client Hello message. Unless Encrypted Client Hello is used, that name is visible to anyone on the path: your ISP, your employer, a public Wi-Fi operator. Censorship systems often block sites by matching the SNI field.
Why it matters
SNI is why HTTPS hides what you do on a site but not which site you visit. A VPN moves that visibility from your local network to the VPN server; ECH aims to remove it for supported sites.