With so many technologies, blockchains and platforms out there, it is easy to get isolated in one and lose access to the others. For example with the rise of smart contracts, BTC didn't have as much utility in the DeFi space. Here we have a good example of a wrapped token, wBTC, which is an ERC-20 token that mirrors BTC and makes it compatible with the ethereum blockchain. It opens the door to things like lending for investors that want a "mirror" of BTC on ethereum's DeFi protocols, turning BTC into a yielding asset in thing like liquidity pools.
The 1:1 ratio is usually kept by the wrapping process. Usually, we have what are called "merchants". When you want to create a wrapped token, say wBTC, what you would do is send 1 BTC to the merchant and they would mint a wBTC to match that BTC you sent. In case that you want to have that BTC back, you would burn the wBTC you have and the merchant would return that BTC to you. This is pretty much identical to how pegged stable coins work.
Even though wrapped tokens have a ton functionality and add flexibility and liquidity to DeFi, they are not a perfect solution. The biggest set back in my opinion is the centralization that naturally occurs when wrapping a token. You would have to entrust the merchant with your funds and also entrust them during the minting process.
Other than wrapped versions of BTC such as wBTC or renBTC, which are just a way of transporting BTC on to other non-native blockchains and ecosystems, we also have an interesting case when we are considering other types of wrapped tokens such as wETH. In the case of wETH, this token allows us to trade a synthetic version of ether on the ethereum blockchain. wETH is also an ERC-20 token. ERC-20 is a token standard, which you could say is a set of rules that defines how a token should act. Ether, the native token of the ethereum blockchain, isn't a ERC-20 token and thus not compatible with protocol that work on ERC-20 tokens. So, wETH is a tradable version of ETH for such circumstances.
Unlike wBTC, wETH isn't "wrapped" per se. Rather you swap regular ETH for wETH via a smart contract. The team behind wETH have stated actually that they hope this token becomes irrelevant, either by an update to ethereum's base to make ether more versatile or changes in how ERC-20 tokens are defined and used.