We're basically out of IPv4 addresses. There are only 32 bits dedicated to IP addresses in IPv4 -- which corresponds to about 4 billion possible IP addresses -- and we've more or less assigned them all. You can't add more computers to the internet without weird hacks.

IPv6 quadruples the number of bits used for addresses (i.e. it's got 128-bit IP addresses) -- every person on Earth could have an IPv4 internet's worth of IP addresses and you still wouldn't be anywhere close to exhausting the address space.

Unfortunately, IPv6 was not designed to be directly backwards compatible with IPv4 and it has a bunch of other changes besides just making the addresses bigger. So, even though it was introduced ~30 years ago, it's still not supported everywhere...