My sister 
In case you use another term, earworms are songs, tunes or beats that get stuck in your head, constantly. Often it takes a night's sleep to get rid of it, but even then you may wake up to the tune rattling around in there and you suddenly feel like death isn't such a bad idea.
WHY? Read on.
History
The term 'earworm' comes from the German equivalent 'Ohrwurm' which is what they called Earwigs. After drying and grinding earworms up, they were used to treat ear diseases, and over time was Latinized, and through a kind of series of Chinese whispers, was described as 'worm that enters the ear', and then 'earworm'.
This term was then popularized by an article written by Stephen King of all people in the 1980's. So it's really quite a recent term.
But music has been around much longer than that, surely it got stuck in people's heads then, too? Centuries ago the term was in fact 'The piper's maggot', which I might start using from now on.
Involuntary Imagery
The professional term that nobody uses is 'Involuntary Musical Imagery', which struck me as an interesting term. 'Involuntary imagery' seems to be a fairly common thing in us humaans. How often have you found yourself thinking with a strong image or place or person in your head seemingly without any trigger?
It turns out about 30-40% of our conscious thoughts are involuntary. Why? That has yet to be answered for certain, but in one study it was found that there was a significant connection between involuntary memories and people who have a vocal stutter:
Significantly more stuttering participants than control participants indicated both recurrent imagery and associated memories.
Not only this, but the thematic nature of those stutter memories were full of anxiety, negative social situations, shame and sadness, usually based on events from their childhood. The more involuntary memories of these negative events, the more likely they are to have a stutter.
This struck me as connected to earworms since they are simply conscious thoughts brought to us involuntarily, too. Thankfully for researchers, around 90% of people get earworms at least once a week, so it's a pretty easy place to start studying.
Catch!
Now it might seem pretty obvious how songs get into our heads. Typically it's songs we like, or failing that simply a catchy song that's easy to recall. You may also be aware of songs that seem to attach themselves to a memory, so whenever you recall that memory, the song is dredged up with it, and vice versa.
I involuntarily experimented with this just now. I took a break to make a snowman since it is snowing here in Shanghai for the first time since I've lived here, 4 years or something. And I hadn't seen proper snow at all since about 2010. As I ambled past the busy roads, the song driving home for Christmas by Chris Rhea ended up in my head, and it's still there now, the same 15 seconds or so on loop.
This makes total sense. Snow is associated with Christmas, that song is associated with Christmas and cars, and it's a catchy song from my childhood.
What song does this trigger inside you?
But what makes a song catchy? Ol' reliable researchers got into this, too.
It was found that music with quite close musical intervals and long notes are quintessential features of earworms. When looking at thousands of earworms reported on the now deceased website earwormery.com, there was a clear pattern of long notes and small intervals in most of the songs there.
The Zeigarnik Effect
This effect, named after the Psychologist who studied it, Bluma Zeigarnik, states that people tend to remember unfinished tasks better than completed ones. Bluma noticed one time that a waiter had a better memory of orders that were unfinished to those that were complete. Experiments were built on this premise and suggests that the brain prioritizes incomplete tasks and throws away those that are complete. Earworms could be the results of being an unfinished task.
This has come under controversy over the years, with other researchers finding it hard to replicate, but it does fall in line with Lewin's Field Theory which states that a task already started goes through cognitive stress or task-specific tension, allowing easy access in the mind. This tension is then relieved upon completion of the task, shutting down that accessibility.
A Remnant of Learning?
It may seem that the Zeigarnik effect, catchy tunes and involuntary imagery come together to create an unimportant side effect to annoy you, but there's more.
Earworms could actually be a remnant of how we used to learn before writing existed. Passing information from one generation to the next couldn't have been on paper, but it could have been memorized by repetitive song which uses multiple senses and muscles, to rub it deep into our memories. Kind of like making a little chant to remind yourself to get your wallet, keys, phone, bag, computer and underwear before you leave the house. Or the alphabet song.
As a consequence, the brain has numerous ways to access that earworm; vision, audio, movement, even breathing if your brain somehow relates a diaphragm movement to a particular long note in a song.
How to Stop Them
This is the same kind of question as with hiccups. There's no surefire way, but there have been some interesting results over the years.
In some cases, they take the approach of the Zeigarnik effect, and by lisitening to the song, giving in to its power, you complete it and the tension is resolved.
In others, you can listen to 'cure' songs, songs thate replace the earworm, but are less annoying or less prone to stick.
Most interestingly, doing moderately difficult puzzles has shown to distract people just enough to get it out of your head. Easy puzzles won't cut it, because it doesn't take enough of your mind power. A puzzle too difficult will make you grow weary and give up, allowing the earworm to return.
A puzzle, especially a word puzzle (since most earworms are lyrical) needs to be just about hard enough to keep you busy, but easy enough to keep your attention.
Try it and let me know if it works!
Hint: It's only in ONE place
Part 2
I've noticed I still have a lot of tabs open on this subject that I'll try and organize into a second post tomorrow. There have been a lot of interesting research, and as you can tell from this post, there are several possible causes and effects to take into account.
but for now, thanks for reading!
All images CC0 licensed
References: Earworm History, merriam-webster | Recurrent involuntary imagery in people who stutter and people who do not stutter | Zeigarnik Effect | Lewin's Field Theory | NY Times | Scishow