TIS and CryptoCard authentication are (despite their names) generic forms of simple challenge/response authentication available in SSH protocol version 1 only. You might use them if you were using S/Key one-time passwords, for example, or if you had a physical security token that generated responses to authentication challenges. They can even be used to prompt for simple passwords.
With this switch enabled, PuTTY will attempt these forms of authentication if the server is willing to try them. You will be presented with a challenge string (which may be different every time) and must supply the correct response in order to log in. If your server supports this, you should talk to your system administrator about precisely what form these challenges and responses take.