The warning means that certain passive elements of the page (passive elements are things like images, videos, audio, etc) have been loaded over an insecure connection. No active content, which is content that could access your username or password (primarily scripts, but also iframes), has been loaded over an insecure connection, so entering your password on that page is just as safe as if the warning message was not there.
There are two reasons that browsers warn you about passive mixed content. The obvious one is that an attacker could replace the insecure images with something else. The more subtle risk is that if an attacker can see what images are loaded on the page, they might be able to correlate that with the pages on the site that load those images, and use that to determine what page on the site you are viewing. In your case, that doesn't matter, but for some sites HTTPS is used partly to prevent an eavesdropper from determining which part of a site you are viewing.
If the page has been loaded over HTTPS, and there is mixed active content, which means it wouldn't be safe to enter your password, your browser will block the script automatically, so it isn't a risk. If you decide that you do want the script, it very prominently marks the site as being insecure.
Before loading the unsafe content:
After clicking "Load unsafe scripts":
Provided that the URL begins
https:// and there are no prominent security warnings, it is safe to enter your password.