Gwei is a term used in determining the cost of a transaction with Ethereum. It is the denomination for defining a gas fee.
Ethereum is a special blockchain in that its operation as a programmable blockchain means that there are financial transactions, as well as smart contract ones - but these all incur a fee. This is where Gwei comes into play. One Gwei is equal to 0.000000001 ETH and it is the denomination or price tag of an Ethereum transaction.
When we talk about an Ethereum fee, it is known as a gas fee. Gas is the fee paid for sending transactions on the Ethereum network. This is used if you're sending ether tokens, transferring any other ERC-20 compatible cryptocurrency, or running a smart contract on the network.
The gas fee and the amount of Gwei you pay can vary. Depending on the transaction, you may be able to pay more Gwei for a faster transaction or less Gwei for a slower transaction. It is also important to remember that as a dollar figure, 20 Gwei can be worth something very different depending on how the price of Ether moves because one Gwei is the same as 0.000000001 ETH.
Essentially, if you intend to use the Ethereum blockchain for any of its functions, or even if you are just sending Ether to another wallet address, you will be required to pay a fee - the gas fee - and this fee will be denoted in Gwei. The amount of Gwei you pay for a transaction can vary depending on how congested the market is, and what the price of Ether is.
When the Ethereum blockchain is more congested and busy, the gas price rises substantially thus, performing a transaction at this time can cost much more Gwei than the same transaction at a later, less congested, date.