Modern can simply mean something that is "up-to-date", "trendy", "new", or from the present time.
It can also refer to the "modern age", a very loosely defined time period which generally commences at or some time after the renaissance in Europe. How long after will depend on the specific usage - for example a historian might be referring to the period 1650-, whilst a musician might be referring to music postdating the romantic era, which would date the beginning of mordernity to around 1900.
The modern age may be defined to extend to the present day, or else to conclude with the advent of postmodernism (which may be dated any time from the 1960s to the early 1980s), again depending on the usage. In the case where modern is used in a sense which means "before postmodernism", it may refer specifically to modernism.