An unconfirmed transaction is covered in full under zero confirmation transaction, the more technical name for the same thing. Where that page deals mainly with accepting such payments, this one looks at what happens to a transfer while it waits.
After a wallet signs and broadcasts a transfer, nodes check that it is valid and hold it in their mempool. Block producers then choose which pending transactions to include, usually favouring those paying the highest transaction fee for their size. When the network is busy, a low-fee transfer can wait for hours or days, and some nodes eventually drop it, which returns the funds to the sender's control.
Senders have a few ways to unstick a payment. On Bitcoin, a wallet that supports replace-by-fee can rebroadcast the same payment with a higher fee, and the receiver can spend the pending coins in a new, high-fee transaction so that miners take both together. On Ethereum, a sender can resubmit a transaction with the same sequence number and a higher gas price.
The same flexibility creates risk for the person being paid. Until a payment is in a block, a rival version that sends the coins elsewhere could win, which is the basis of a double spend attack. That is why businesses usually wait for a set number of transaction confirmations before treating funds as received, and accept unconfirmed payments only for small amounts.