Swap like swapping of blockchain e.g from ETH to EOS or to mainnet, it simply means the cryptocurrency is migrating from one blockchain to another (most times from a third party blockchain to their very own blockchain).
Why they (the project/dev?) need to swap the token?
The correct/perfect answer has to come from the project in questions but most time it has to do with taking advantage of the additional features the new blockchain they intend swapping to has to offends and also to take advantage of the hype associate with the new blockchain e.g Binance chain for publicity.
What is the advantage/disadvantage for the project?
They get the advantage/disadvantage associated with the new third party blockchain or their native blockchain (mainnet). For advantage, e.g for tokens swapping to Binance chain they get listed on Binance decentralized exchange and the possibility of getting listed on Binance centralized exchange increases. For tokens swapping to Ethereum blockchain they get the advantage of listing on Ethereum based decentralized exchange which means they get listed on more exchanges.
For disadvantage, token swapping from Ethereum blockchain can no longer be tradable on Ethereum based decentralized exchanges like IDEX etc or used on the Ethereum network. The disadvantage or advantage are associated with the blockchains involved in the swapping process.
You should note though, when projects swap from third party blockchain (e.g eth blockchain) to their native blockchain (mainnet) it's to continue development of the token to bring about mass adoption.