From what I've understood, coins are wrapped to enable cross-chain movements. Let's say you have X BTC, but you want to take advantage of ERC-20 features. You can "move" your BTC to Ethereum blockchain by depositing your X BTC in Wrapped BTC (WBTC) smart contract. It'll lock your BTC, and give you the equivalent amount of WBTC tokens, which are ERC20 tokens on the Ethereum chain.

Wrapped tokens enable use across otherwise incompatible blockchains.

Wrapped tokens are facilitated through a bridge. The bridge contract(s) lock the tokens on one blockchain, and re-issue wrapped tokens on a second blockchain. At a 1:1 peg.

That way the wrapped tokens can be used in Defi or Dapps on the second blockchain, and later (if desired) sent back through the bridge to be “unwrapped” into their original form, on the original blockchain.

This is so cool! I feel like this is the sort of creative enablement that smart contracts bring to the table.

Just note that for now, most of those bridges are custodian. AFAIK at the moment the only trustless one is RenBTC. The more popular WBTC and others are essentially just some trusted entity issuing IOUs when you give them your BTC.