"Modern" is an adjective that describes culture, fashion, ideas, technology, etc. It means "recent" - usually within the past 25-50 years, although for some technology products it can mean as recent as 2-3 years old like:

The computers at the library need to be updated to a modern operating system. They're still using Windows XP.

"Modern life" is a common phrase on its own. It means the way that people live in the present times.