What an IP address is
An IPv4 address is four numbers 0–255 separated by dots, like 192.168.1.10. It identifies one network interface. On a local network every device must have a different IP - two devices with the same address collide, and traffic for that address becomes unreliable.
Private vs public
Some ranges are reserved for private networks (10.0.0.0/8, 172.16.0.0/12, 192.168.0.0/16). They're reused in every home and office and are not routable on the public internet - which is why NAT exists to translate them on the way out.
The subnet mask decides who is 'local'
An address is paired with a mask (written as /24, /25, …). The mask splits the address into a network part and a host part. Two devices can talk directly only if they share the same network part - otherwise the traffic has to go through a router.