Packages of software are signed with a certificate to prove they haven't been modified and come from the original maintainer.

These certificate often have an expiry date, after which they are no longer valid. Your phone fails to install the package then, it assumes its not trustworthy.
Setting your date back to the past tricks your phone into thinking the certificate hasn't expired yet.

Don't forget to set it back to now, certificates are usually not valid for dates before their creation. So websites and newer software may not work/install!