The idea is that you can use short-lived keys, bound to certificates via an ACME-style challenge, but based on an email address. The signature goes into a Transparency log to prove it happened while the cert was valid. Then revocation is no longer an issue.
OTS just depends on the Bitcoin block headers (megabytes/year), and the databases of timestamps maintained by the public calenders, (a few GB/year; it's new entry per calendar per second). It's a more easier to archive a few GB of data than the tens of terabytes in the public CT logs.
Note that OTS proofs do not have any notion of a transaction in them. Rather, they perform commitment operations that end up at a merkle root of a Bitcoin block (at least in the 99.9999% of proofs that use Bitcoin). With the `--no-bitcoin` option, the OTS client will tell you what block # to look for, and what the merkle should be for the proof to be valid.
tl;dr: it proves data existed in the past. In the case of a PGP signature on a Git commit, that can prove the signature (and the repo contents) were created prior to the key being compromised.
1) Mostly, because sometimes you don't know when the key was compromised.