In more detail
IPv4 offers about 4.3 billion addresses; IPv6 offers 2128. Addresses are written as eight groups of hex digits (2001:db8:0:0:0:0:0:1); leading zeros in a group can be dropped, and one run of zero groups can be shortened with :: (2001:db8::1). A single network normally gets a /64, and devices usually build their own address from the prefix the router advertises (SLAAC), often with temporary random parts for privacy. Every interface also has a link-local address starting fe80::. There is no broadcast, and NAT is normally unnecessary.
Why it matters
Most networks now run IPv4 and IPv6 side by side, so firewall rules written only for IPv4 can leave a service open, or unreachable, over IPv6. In URLs an IPv6 address must be wrapped in brackets: http://[2001:db8::1]:8080/.
Example
2001:0db8:0000:0000:0000:ff00:0042:8329 compresses to 2001:db8::ff00:42:8329. One /64 network holds 2^64 = 18,446,744,073,709,551,616 addresses. Shorten or expand an address with the IPv6 Address Compressor and IPv6 Address Expander.