I had a pending transaction pending for days. I was in no rush and was not going to increase the fees. I received a new message when I logged into the wallet today. It stated the transaction was on the local network and needed to be broadcast. I had already broadcast it and signed it days ago. Please explain. Thank you.
Your wallet will broadcast your transaction to other nodes on the network, and those nodes will (most likely) add your transaction to their mempools as it awaits confirmation. If the transaction does not confirm after an extended period of time, nodes may drop the transaction from their mempools - when and what transactions are dropped is a policy that is configurable by each individual node, so ultimately there is no saying exactly when a transaction that is unconfirmed will be dropped from the network (if at all).
I believe the default setting for bitcoin-core nodes is to drop a transaction after two weeks, or once the mempool hits 300 Mb (starting with the lowest fee-rate transactions).
So if you transaction is quite old, or has a fee-rate that leaves it far below the top fee-rate transactions in the mempool, then it may be dropped by a large number of nodes in the network. At that point, your wallet software may prompt you to re-broadcast it, so that it can be confirmed.
Ideally, you would be using a wallet with RBF enabled, so that you can simply increase the fee as necessary to help gain transaction confirmation according to your needs.