[...] I have heard people mention practicing scales, but I don't quite understand what this means. I get the scale part, but why / which / how? [...]
Well, playing up and down scales for the sake of it, without knowing why you're doing it, is not going to help a great deal, so you're wise to ask.
Here's an extremely simplified attempt to explain a bit of the why / which / how thing about scales:
In western music we have what is called a chromatic scale that contains all the notes we use in music. All of them.
Chromatic scale = c c# d d# e f f# g g# a a# b c'. It contains twelve semitone steps. Each note in the chromatic scale is a semitone (1 fret) higher than the last.
For various reasons, certain combinations and patterns of notes are pleasing to the western ear. One of these patterns is the Major Scale - the
do re mi fa so la ti do "tune" that most will be familiar with is a major scale.
Now, most singers have a certain range within which their voices will reach. Some instruments are made to favour a certain key (Irish tin whistle, for example). In order to suit a singer or a choice of instrument a tune will often be arranged in a specific key. Common keys are G major and C major - they are convenient to play on guitar and 'ukulele. The are also quite far apart in pitch, so it is likely that a versatile singer will be able to manage a song in one or the other of those keys.
In Irish traditional music the keys of D major and G major are very common - largely because they suit the instruments used in that genre.
In bluegrass music the keys of G major and A Major are most common. They suit banjo, mandolin and fiddle well.
Depending upon the genre of music you play, and the instruments commonly used for it, or upon the pitch/range of your (or your singer's) voice, you are likely to find yourself playing in some keys more than others.
In each key, a certain selection of notes from the chromatic scale is used, and that selection is different for every key. By knowing the scale for that key you will be able to find the notes that are in the key, and miss out the notes that aren't. If you are playing a song in C major, you will mostly avoid sharp or flat notes, as there are none in that key. If you play some by accident, then they may sound out of place or out of tune.
If you know how the scale for that C major key fits onto the fretboard then you have a kind of map to the right notes. If you try to improvise a solo the scale gives you a framework to guide you. Similarly, if you play by ear, but are not 100% sure which fret will give the next note you want, knowledge of the scale will often remove uncertainty. "That fret there isn't used in the scale for this key, so the fret I want must be
that next one!"
Scales in isolation are of limited use. You need to learn how they fit into the music.
The best way to learn scales is to learn the patterns they make, rather than the notes. That way you can move the patterns around and get the scales for different keys.
Once you know the patterns, you will start to recognise how melodies fit into those patterns. As you play a tune, see how the notes you fret correspond to the scale patterns you have learned. Gradually an association builds up. A partnership between ears, fingers and eyes.
As you get more experienced, you start to learn how scales work with chords, and you begin to recognise and understand the way that specific notes in a scale or chord contribute to certain flavours and effects in the music.
Scales are an important part of the jigsaw, but just a part.
Scales I would recommend learning first (without knowing about your musical genre or voice) would probably be the C and G major scales, the C and G major pentatonic scales and the Am and Em pentatonic scales. You have to start somewhere, and I find those get a lot of use.
It's a very basic explanation, oversimplified, clumsy and incomplete, but I hope it makes some kind of sense.
