any of the ridges of wood, metal, or string, set across the fingerboard of a guitar, lute, or similar instrument, which help the fingers to stop the strings at the correct points.
Frets are a crucial part in a beginner guitarist learning process and the world of guitar in general. Frets are used as a way of knowing what note you are playing to make sounds that are pleasing. Frets are the way guitarist play guitar, they memorize finger placement on the 6 strings on various frets to learn Chords or a really cool riff in a song.
Frets are so important in the guitar world because the way most people learn guitar is "un-traditional". For example, when people learn piano they learn notes ( C, C#, D, D#, E, F, F#, G, G#, A, A#, B) and even though people who play guitar know what notes are we don't learn songs by notes. A lot of guitarist learn by Tab.
"Tabs" as they are known in the guitar community is a way to learn more riff heavy songs, for example City Of Stars from La La Land. You can also learn the chords to chord heavy songs like Love Yourself by Justin Beiber, but learning chord heavy songs is easier than learning riffs. Tabs can still help you learn Chords though, through this diagram you can see what a C chord looks like.
Through tab you can see the opening riff City Of Stars
The tangent line is a pattern that guitar luthiers use to determine fret placement. This pattern is based on an angle that "cuts" the fret board in half diagonally, this line is used to make 90 degree angles so as the frets get closer to the bottom of the scale the will get skinnier.
So do frets matter? to put it simply yes they do matter a lot. Its a guitarist way of knowing what their playing is sounding good. Its also their way of learning new songs or riffs, its their way of knowing the chords their playing are correct. Now to make this answer complicated once you're a very advanced guitarist frets don't matter and some guitarist take up the challenge of playing fret-less guitars. There is a reason why people don't play fret-less guitar, your muscle memory has to be perfect. Fret placement is also very important because it makes everything sound better, now while normal fret placement doesn't make perfect notes it is always very close to perfect.