Probably 'signature check failed' - but could also be 'signature check timed out'.
The first means that BattlEye compared a 'fingerprint' (the signature) of your client-side game-files and found they didn't match what it expects to see. Possibly a sign of corruption, or a missing file, or worst-case, something there that shouldn't be there, like a virus or a game-hack-script.
Signature-check timeout is simply just that BattlEye on the server couldn't establish contact quickly enough with BattlEye on your game, and gave up trying. This could be because of lag (high ping) between you and the server, caused by congestion at either end or in-between. It can sometimes happen if there is a lot of traffic going on at either end, such as you running a bandwidth-hungry program at your end (torrent programs or streaming Youtube videos are often a cause of this kind of timeout, but I can just as easily happen if your household bandwidth is all used by by people Skyping and downloading Sky/Netflix vids at the same time). Alternatively, if the game-server is busy trying to log several people on all at once, and one or all of them are slow, or the game itself is heavily loaded (many people on), then sometimes one or more of the 'would-be joiners' will timeout. Because our BattlEye cannot 'talk' to your BattlEye to prove to itself that all your files are 'clean', it drops you, in order to protect the server. Usual remedy for this is simply to try again. Usually you will get through.