OpenSSH pulled in libsystemd to provide startup notification. Libsystemd pulled in liblzma. No code from liblzma normally ends up in OpenSSH. But because it is built as a dependency for libsystemd, it's build scripts are ran in the same environment as libsystemd, and OpenSSH.
The attack payload was hidden as an obfuscated binary blob in the liblzma tests directory, masqueraded as a compression test case. When lzma was compiled from the git sources, generating the build scripts using autotools, nothing untoward was done. But lzma was also provided as a source tarball that was used by distro packagers, that had the autotools already ran. The attacker replaced the autogenerated, unreadable script output with one that checked if liblzma was being compiled in the same environment as OpenSSH and if it was being compiled so that it was going to end up as a .deb or .rpm package, and if both were true, embed the attack payload into OpenSSH.
Then the attack payload started with a lot of checks, including testing whether OpenSSH was being started normally by init scripts or manually, and for the presence of usual debugging tools, and only attached the payload to the running process if it seemed like a "natural" bootup with no running debugging tools. When running, the payload hooked into private key verification, and if the correct private key attempted to login, the payload would take the rest of the incoming packet and call system with it, that is, provide remote code execution as root.