Modern has it's roots in latin word modo meaning "just now". But almost everything that is named "modern" today refers to something relatively old.
Modern is so inflated that there is actually another term in history defining more closer to current day events than what's thought of "modern history". Yet, even this contemporary history (or current history) spans back to the last century.
At some point all those modern things will probably get named something more historically accurate and the term modern is once again pointed to something more close to the current affairs. It might even catch up for a while until it inevitably starts to fall back again.
Of course a century back is just s blink of an eye in grand scale of things. Modern geological eras span hundred of thousands of years back. So maybe it's not that bad to refer something as recent as last century as modern times. There is just so much more documented history happening in this modern time that every year could warrant it's own named period. And while things keep speeding up soon even that wouldn't be enough.