Bitcoin is a peer-to-peer gossip flood network. Whenever a Bitcoin participant creates a transaction, their wallet software submits it to its peer nodes. These peers then relay it to their peers in turn. The transaction floods through the network and reaches most nodes. Eventually, the transaction is included in a block which makes the transaction part of the committed history of the network. Blocks have propagation guarantees, because the blockchain is the mechanism for nodes to converge on a globally shared state. Now, every node is guaranteed to get the transaction since they will get the block.
So, each transaction originates from the sender's node, and eventually, every participant's node will have a copy of each confirmed transaction.