Every node in the Bitcoin network acts independently. When a node hears about a new block, it will perform a series of checks to see if it is valid according to the network's rules.
If the block is valid, the node adds it onto its a local copy of the blockchain and broadcasts the block to the other nodes it's connected to.
If the block isn't valid, the node will reject it, and not broadcast it.
So by following the network's rules, even though each node acts independently, together the network is able to remain in consensus regarding the blockchain history.
I hope this explanation will help you.