work fine in Mozilla – not so fine in Explorer

my webpage works perfectly when I open it in Mozilla.

however when I open my webpage in Explorer some of the features don’t work(e.g. the drop down menu, feature items are not displayed properly, etc)

when I access the WP admin page from Explorer, I get this message on the dashboard: “It looks like you’re using an insecure version of Internet Explorer. Using an outdated browser makes your computer unsafe. For the best WordPress experience, please update your browser.”
This message does not appear when I open the WP admin in Mozilla.

My webpage used to work without problems in Explorer and then it stopped.

any advice? Thanks in advanced!