You could get a clear idea on how provably fair works in a dicesite from
hereHow does provably fair work?
Although there are several implementations of the provably fair method, we will describe the most common one. With this method each roll-result is calculated by the following variables:
Serverseed - provided by the gambling site
Clientseed - provided by your browser and adjusted by you
Nonce - A number that increases with each bet you make
You will get an encrypted hash of the serverseed before you start gambling. Since you get it in advance, the site cannot change it later. However it is encrypted, so you cannot calculate your own roll results in advance (only afterwards if you get the unhashed serverseed.)
Your browser will generate a random clientseed. However, you could and should adjust this clientseed before you start. This way you can make sure the site does not know your clientseed in advance.
Now if you make a bet the nonce starts with 0 or 1 depending on the website. After each bet you make, the nonce number will go up by 1.
So coming to your question regarding the purpose of Client Seed, let's assume that there is no client seed but only server seed and nounce taken for output calculation. You play several rounds and lose heavily so you change the client seed, once again you lose without any profits. If that's the case, what will you tell others? You'll most probably tell that site only gives bad seeds and that they are programmed to incur hefty losses or that the site is scam.
But by providing client seed(which could be adjusted by you) you are deciding the server seed's outcome not the gambling site. The server seeds outcome varies with the client seeds you use. So you can't actually blame the site being unfair to you.
To sum it up, Client seeds are made available to show that the site is being fair or say to build users trust.
