Blockchains such as Bitcoin, Ethereum, and Ethereum Classic accept new transactions so people may move cryptocurrencies from address to address or to use smart contracts or dapps in the case of Ethereum and Ethereum Classic.
In most blockchains users have to pay a fee per transaction so that miners or stakers include them in blocks and then are executed and included inside the blockchain.
In the case of blockchains such as Bitcoin, that only have accounts and balances, the transaction fee is just a straight forward amount you add to the transaction amount you want to transfer. For example, if you want to transfer 1 BTC to another address, you just add something like 0.0001 BTC (this is just an example, fees may vary) in the "fee" field and the blockchain will process your transaction and transfer the fee to the miner's account for a total debit of 1.0001 BTC from your account.
In the case of smart contract blockchains such as Ethereum and Ethereum Classic, each transaction uses up what is called GAS and GAS has a market price that is paid to miners or stakers. For example if a dapp transaction uses 100,000 in GAS, and the price of GAS is 0.000000181 ETH (this is just an example, GAS prices may vary), then the transaction fee will be 100,000 x 0.000000181 = 0.0181 ETH. So, if you are going to use 1 ETH in that transaction on that dapp, the total cost will be 1.0181 ETH. This is the amount that will be debited from your account.
Transaction fees are paid to miners or stakers who are the block producers in blockchains such as Bitcoin, Ethereum, and Ethereum Classic.