SegWit is a successor to BIP 62 -- BIP 62 wasn't good enough, it very likely would not have fixed malleability conclusively.
SegWit has a new limit called weight -- Normal bytes are 4 weight units. Witness bytes are 1 weight unit. -- The limit of weight units is 4 million
Signature hashing before SegWit is stupid because you have to resign it for every signature because each key has a different version to sign (BIP 143)
SegWit adds input value into transactions, so fees and inputs are signed along with everything else. This prevents being tricked into signing a very high fee transaction.