Why is the block height 627810 on the Bitcoin Testnet? Are there information out how and why this happened?
This block height is far ahead to the Mainnet block height.
EDIT: maybe someone put large hash power on the testnet3 and solve a lot of blocks in no time before a diff adjustement happened?
Pretty much. The difficulty on the testnet is much lower than the mainnet, and it resets back to the minimum if no block was found in some time. I think a couple months ago someone was mining tons of testnet blocks trying to push it to go past the second halving for some reason.