Nodes serves as gateway to the mempool[1] so there is a need for nodes to share their mempool with each other in order for other nodes (peers) to perform its own check for the validity of transactions.
If the transaction passes the node's checks, the transaction is added to the node's mempool. That node will also broadcast it to other nodes, called peers. Each of these peers will perform its own checks adding valid transactions to its mempool and then broadcasting the transaction along to its peers.
Here is a good presentation by Babypips about mempool and node[2]
It was stated that every node on Bitcoin network share information about new transaction, since transaction is not directly added to the blockchain they are first collected and stored at mempool. Then these nodes communicate with its peers to check the validity of transaction on the mempool.
[1]
https://www.blocknative.com/blog/mempool-nodes[2]
https://www.babypips.com/crypto/learn/what-is-a-mempool#:~:text=Also%20known%20as%20%E2%80%9Cmempool%E2%80%9D%20for,to%20a%20newly%20created%20block.