What is a non-custodial Crypto Wallet?

Could you elaborate on what a non-custodial crypto wallet is? As I understand, traditional crypto wallets involve third-party custodianship of users' funds. So, a non-custodial wallet must differ in some significant way. Does it mean users have complete control over their private keys? Does it offer any advantages compared to custodial wallets? And, most importantly, how secure are these wallets in terms of protecting users' funds and data? I'm interested in learning more about this concept and its implications in the cryptocurrency space.