Good to know
Why doesn't it match my computer's address?
The address your computer reports for itself (for example 192.168.1.20) is a private address that exists only inside your home or office network. Your router replaces it with the public address shown above for outgoing traffic. Every device behind that router shares the same public address.
IPv4 or IPv6?
Four numbers separated by dots is an IPv4 address; a longer string containing colons is IPv6. Most connections still use IPv4. If an IPv6 address is shown, your provider routed this visit over IPv6; you will normally have an IPv4 address as well.
Will it change?
Most home connections are assigned a dynamic address that can change when the router reconnects or the provider reallocates it. Business connections and servers usually have a fixed address. If you use a VPN, the address shown is the VPN server's, not your own.
From a terminal
curl whoismania.com/whatsmyip returns the address on its own, and whoismania.com/api/ip returns the details above as JSON. Both are free to use in scripts at a reasonable rate.