Every transfer gets a fingerprint, a long string of letters and digits. It is computed from the content of the operation itself, so no two IDs are ever the same and an ID cannot be faked to match another transfer.
Where to find it
In your wallet or on the exchange, in the details of the outgoing operation. It is usually labelled «hash», «TXID» or «transaction ID».
What it is for during an exchange
It turns «I sent it» into a verifiable fact. If a payment has not shown up, the ID lets you establish within a minute what happened: the transfer is not yet confirmed by the network, went to another address, or went to another network. Without it, the search comes down to guesswork.
Where to check it yourself
In the explorer of the network the transfer used: tronscan for TRON, etherscan for Ethereum, bscscan for BNB Smart Chain. Paste the ID into the search and the page shows the status: «success», «pending» or «failed».
What the statuses mean
Success, but the recipient sees nothing. That means the funds went elsewhere: compare the address and network on the transfer page with the ones the recipient gave you.
Pending. The fee turned out to be below the current one, so you either wait or speed it up.
Failed. The transfer did not go through and the funds stayed with the sender; the fee is usually still charged.