Modern password management services are incredibly secure, with client-side encryption of your secrets, among other protective mechanisms (to guard against keyloggers, stolen computers, ...)

There is still a risk, because you're trusting third-party software (which in some cases is closed-source – including 1Password), but for most people that is a much lower risk profile than if they were managing passwords themselves.

For specifics on 1password's security, check out https://1password.com/security/