The proposed alternative was Bitcoin Cash, which has a larger blocks and can handle more transactions per block. This meant a hard fork.
It also solved the malleability issue, where people could go in and change a tiny bit of information in the transaction –namely, the signature– in order for its transaction ID to change.
Segwit fixed the malleability issue, in which unconfirmed transactions could be altered. The Lightning network required this issue to be fixed, so that it could pave the way for direct, off-chain transaction channels between wallet owners.
(I found this to be a good article about Lightning and what is does.)
No, it’s a soft fork, so people can choose whether to use it or not. However, it removes the fraud sensitivity so it makes sense that people would choose Segwit.