Please know that this is a good question. We are contemporary to modern times. No one should be sneered at for not knowing that The Art World has its own separate definitions for each of these terms. In any other instance, the English language pretty much allows for "modern" and "contemporary" to be swapped at will.
As you have doubtless guessed, the single most important thing anyone needs to know about Modern Art is that it's different from Contemporary Art.
A good rule of thumb is:
- Modern Art: Art from the Impressionists (say, around 1880) up until the 1960's or 70's.
- Contemporary Art: Art from the 1960's or 70's up until this very minute.
Here at About Art History, Modern Art starts as the Impressionists were winding down. While this is acceptable, strong arguments can be (and have been) made that Modern Art began at a variety of different dates. Depending on which survey course a person takes, Modern Art is said to have begun with:
- Romanticism, in the early 1800's,
- Realism, in the 1830's,
- Daguerre's announcement, in 1839, that he had invented a method for making a direct positive image,
- The writer Baudelaire who, in 1846, called upon artists to "be of their time",
- The first Impressionist show in 1874 or
- The "-isms" of the 1880's (Tonal-, Symbol-, Post-Impression- and Neo-Impression-)
Which one is right? Well, none of them are "wrong". (Here, it was simply a case of "1880" working out well, for me, in terms of organization.) For simplicity's sake, let's just say that Modern Art began in the 19th-century, and ran through a whole slew of "-isms" up until the end of the 1960's.
Regardless of chosen starting date, the crucial factor is that Modern Art means: "The point at which artists (1) felt free to trust their inner visions, (2) express those visions in their work, (3) use Real Life (social issues and images from modern life) as a source of subject matter and (4) experiment and innovate as often as possible."
Wordy, I know! Art is kind of messy that way. It's often easier to make it, than to try to explain it - and making it can be about as easy as childbirth, some days. But that's Modern Art (and Modern Life) for you. Say, now that you're positive of the meaning, why not go have some fun poking around in all of those delicious "-isms"?
See also: What is "Contemporary" Art?