Any stringed instrument with frets has a scale length. And long story short, the scale length is the distance between the nut and the bridge/saddle. It determines the placement of the frets for proper intonation, tone, string tension, and tuning. Now that is not all that scale length determines but the rest is slightly complicated and applies more to crafting a guitar rather than playing one.
Now first off is string tension and how it relates to scale length. A quick example of how these two relate is this, if you have two guitars, one with a lower scale length then the other and put 12 gauge strings on both. The one with the lower scale length is going to be more floppy or loose. Now is the relation between scale length and tone. Some guitarist like using a lower scale length for better playability and some use a larger scale length to achieve a thicker tone. For instance, take two identical electric guitar bodies, one fitted with a 25 1/2″, and the other with a 24 3/4″ scale neck. If you find your technique requires using .009 – .042 gauge strings on the long scale, you’ll probably get the same feel utilizing a heavier .010 – .046 gauge on the short scale instrument, The heavier gauge strings will also have the side-effect of inducing more voltage in your pickups, resulting in a “thicker” fundamental note, and more output.
Comfort and playability is also a factor when it comes to scale length. Everyone is different and that means we all have different hands and arms! Someone with short arms and fingers may prefer a smaller scale length then someone huge like Zakk Wylde. It’s all about personal preference... and as long as you’re playing what you’re comfortable with and can enjoy your session then that’s all that counts!
Here is a picture with three different guitars, all with different scale lengths