rebroadcatsing a transaction with a low mempool presence could speed the confirmations up
When you broadcast a transaction you send it to the network, which means for example you send it to Node_1 (which you are connected to or push tx to) and if that client accepts your tx, it becomes a part of its inventory (has the tx in its mempool). then Node_1 sends your tx to everyone that asks for its inventory or connects to Node_1.
So if Node_2 and Node_3 are connected to Node_1, they now have your tx too. (total 3 nodes).
Then they give it to Node_4, 5, 6,... and in a short time all the network has your tx.
However as I mentioned in the start, that Node has to accept your tx. Sometimes they reject it because for example it has low fee, it is a double spend, ... so your "tx mempool presence" goes down.
You can actually try it next time to get how long it takes for your tx to propagate through bitcoin network (it is a couple of seconds most of the times). Use your wallet to broadcast the tx and then copy the rawTx and push it in any of these services, you will see that by the time you copy and past and click push they all have your tx and give you an error indicating it already exists.
https://blockchain.info/pushtx
https://live.blockcypher.com/btc/pushtx/
