Let's say I have 10 miners node in my network. Once a transaction is initiated, all nodes will be informed about this and then they start mining. 1st node has highest computational power and finished mining the block before other nodes do. Now, will other nodes continue to mine the same block or they will stop mining after 1 st node has finished mining.
It will continue to mine, even after the 1st node has finished mining, until the broadcast of the 1st node is received via the network.
The process of mining a block is essentially trying to come up with a solution to a very complicated mathematical puzzle. The algorithm has been designed in such a way that it is very hard to find the solution to the puzzle, but once a solution is found, it is extremely easy to verify that the solution is correct. So when a miner successfully finds a solution to the puzzle, it will be broadcast to the network and every other node on the blockchain will stop mining and verify that the solution provided is correct. If the solution is in fact correct, the block will be added to the blockchain and the miners will begin working on the next block. If the solution is invalid, then all nodes will continue working on the same block.