Everyone has stereo earphones or headphones. There is a small R and L or something to that end written on these things, to signify which one goes in which ear.
There’s really no huge deal about this. Most of the time, it will not matter how you wear them. Let me list briefly why:

1. The universe is mostly left-right symmetric.

   Parity is not broken in everyday life, so unless you wanna hear a beta-decay electron spinning away or something, you may wear your headphones any way you wish.

   Okay, that was mostly a joke.

2. Some of the music you hear is mono.

   Stereo headphones are meant for stereo audio. If the audio you are listening to has only one channel (although this is increasingly rare in audio produced nowadays), then there is no information for the headphones to stream into different ears, so you hear the same thing through both ears.

3. The rest of your music is stereo, but it makes no difference.

   The information coming through the two audio channels are different (sometimes in a very carefully calculated way, as for binaural sound that simulates spatial distance and directionality). But it doesn’t really matter which one is going in which ear, unless it’s some song where a guy in the left channel’s humming ‘left, left, left’ and a girl in the right channel’s chanting ‘right, right, right.’ In which case it doesn’t matter whether you listen to the song.

4. In most movies you watch it won’t make any difference.

   Although the audio will probably be stereo, there isn’t too much difference in the two channels. Except in some scenes where a guy enters from the left and the sound of the door comes in louder through the left channel. But these are rare in distributed copies of movies, and will usually be taken care of for you in movie halls.

So if the writing on your headphones has worn out, don’t worry, they were of almost no use.