The client seed is a value you supply that goes into the round's result calculation together with the server seed. In most games you can enter it yourself; in some it is generated automatically, but it must be changeable.
Why it is needed
Without your input the result would be decided by the casino alone. Even if it is honest, you could not prove it. The client seed makes the result a joint decision of two parties: neither can choose the outcome on its own.
In practice it also protects against a long-term pattern — the casino cannot pick a sequence of server seeds that works against your particular bets, because your seed is unknown to it.
How to use it
Enter something you chose yourself — any text will do. Change it from time to time: a rotation closes the old seed pair, reveals the server seed and lets you complete the check. See the verification steps described under hash.
Warning
If a game does not allow the client seed to be changed, it is not a complete provably fair scheme. The badge may be on the page, but the check cannot be finished — and that is exactly what most players never check.