That’s how modern music is mixed. In the old days it would be mono and have all the sound coming out of one side. What your describing is in stereo

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Modern audio recordings are recorded in stereo (having a left and right channel). The headphones replicate these sounds appropriately.

Because the audio signal is either sent to the left or the right.

Wired headphones have 3 or 4 connections in the jack left, right, ground, and mic. When an audio track is made part of the recording is the balance of left and right channels. So if you make a song you could say all drums always come from the left, then when you play it back it would send drums down the 'left' wire.

Wireless headphones are the same idea but with radio waves instead of wires, sometimes there's a wire through the headband, sometimes it's another tiny radio going through your head so that left and right talk to one another.

This idea is generally referred to as "audio channels" surround sound systems can be 5, 7, or more channels, with movie theaters being 20 or more, with subwoofers getting special notation and their own channel 5.1 meaning 5 channels (left, right, center, back left, back right) and one sub woofer for deep bass. Again which sound goes to which speaker depends on how the audio was mixed when recorded. And all a mixer is doing here is directing audio 'traffic' to the different channels the creator wants

Building on this, at a live concert, sounds arrive from different directions.

Violins are usually on the (audience's) left, cellos on the right. Singers are often arranged from left to right from high voices to low.

In performances of a particular work, I'm used to hearing the trumpet solo from the right, but in two performances this year it (and the drums) came from the left.

You may also be thinking of binaural recording.

The BBC recently reported on a podcast series titled The Dark is Rising that uses the recording technique.

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If you look at your headphone jack, you may notice there are black rings on it. Those rings separate different channels. One ring means only one channel (one channel and ground). Two rings means you have 2 channels (left, right, and ground) and 3 rings means there's an additional channel for a microphone.

Sending different signals down the different channels means each speaker plays a different sound. By changing the relative volumes (and timings by a very small amount) our brains are tricked into thinking the sound is coming from a certain point in space, including moving from one side to the other.