Im curious what will happen with my multibit client when a fork happens?
It will choose the fork that uses the original protocol unless it is upgraded to new code that chooses the fork with the updated protocol.
Does this mean that multibit also needs to be updated aswell as Bitcoin core ?
That depends on which fork you want to be on, but in general if there is an intentional fork in the bitcoin protocol to fix some issue, and you want to be operating on the new fixed protocol, you'll need to update.
When we say everyone agrees, how do I agree?
You agree by choosing software that implements the protocol that you agree with. 99% of the altcoins are all essentially bitcoin forks that fork off at the genesis block of the blockchain. If you agreed with the decisions made by the developers of those forks, you'd choose to run the software that was written for the fork you liked (litecoin? dogecoin? etc). By choosing software that is compatible with the current bitcoin protocol, you have chosen to enforce the current rules of the bitcoin protocol.
If the bitcoin protocol were to fork, and some people chose to continue running wallets that supported the old protocol rules, then there would be an "old bitcoin", and a "new bitcoin". Since the blockchain would fork later than the genesis block, any bitcoins generated prior to the fork would be spendable on both forks. Bitcoins generated after the fork would only show up on the fork where they were generated. If a single transaction spent pre-fork bitcoins and post fork bitcoins together, then all of those bitcoins would only be spendable from the side of the fork that the post-fork bitcoins came from, from then on.
What do I need to do, I don't run a full node nor do I use Bitcoin Core wallet.
The reason that your multibit wallet only sees bitcoin transactions, and not any other altcoins, is because it is designed to implement the current bitcoin protocol. If there is a fork in the bitcoin protocol to fix some issue, and you want to continue to operate on that new fork, you would need to wait for the MultiBit developers to update their software, and then you'd need to upgrade.