Google is urging users to activate its Enhanced Safe Browsing feature via numerous alerts in Gmail that keep coming back, even after you acknowledge them.
The difference between the two security features is that Safe Browsing will compare a visited site to a locally stored list of domains, compared to Enhanced Safe Browser, which will check if a site is malicious in real-time against Google's cloud services.
While it may seem like Enhanced Safe Browsing is the better way to go, there is a slight trade-off in privacy, as Chrome and Gmail will share URLs with Google to check if they are malicious and temporarily associate this information with your signed-in Google account.