On a guitar, the fret board is the long neck of the guitar stretching from the body up to the very end, where the strings are tightened. This long neck of the guitar is where the secondary hand plays the chords by pushing down the strings against the fret board in specific places. By pushing the string down against the fret board, effectively the length of the string has been shortened.
When plucked, hit or strummed, the vibration or frequency of the strong, which is what creates the specific note, is changed depending on its length. So, a longer string will create a lower frequency and so a lower note, whereas a much shorter string will vibrate very quickly, and so have a high frequency, which produces a high note. A single string can produce a wide range of notes, depending n where the string is pushed against the fret board, and how much it has been shortened by. Of course, the thickness of the string, and even what it is made from will also have a big influence on the sound, the frequency, and the quality of the note, and on a standard guitar the strings are made using either a combination of different thicknesses, or even a combination of different materials too.
This provides the range of notes, whether shortened or note, that you here when the guitar is strummed. The frets are the small, usually metallic strips which run all the way down the fret board. These act as ridges, so that when a string is pushed against the fret board, the frets act as the points at which the string is shortened. Otherwise there could be slight variations in where the finger is pressed on the string, which could affect the note. Therefore, as long as the finger is pushing against the string somewhere between the two frets required, the lower fret, or one nearer the body of the guitar, will pick up the string and act as the catch point, shortening the string to a specific length, and resulting in a clear and exact note.
These frets are usually made from nickel alloy, although sometimes they are made from stainless steel. They are usually made from metal to provide a firm and exact resistance, and are placed along the fret board at very exact points, according to some pretty complex mathematics involving frequencies and pitch. Each fret along the fret board is considered to be a half step interval as far as the scale of notes is concerned, and on a standard classical guitar there will be a total of 19 frets, and so 19 half steps along the scale. Electric guitars usually have more frets, usually between 21 and 24, meaning that their range is usually anything up to five half step, or two to three notes greater than that of a classic guitar.
The frets of a guitar, whilst generally fairly standard, can vary slightly to provide extra features of playing styles. For example. There are frets known as jumbo frets, and these are much wider, or thicker, than standard ones. This extra thickness means that the player can use a vibrato technique, achieved by pressing the string down firmly, then releasing it slightly, then pressing firmly again, very quickly in succession. Taking this vibrato technique even further, there are fret boards which, rather than having frets attached, have them formed from the board itself by having the space between the frets carved away, and this provides a very dramatic effect when the vibrato method is applied. Generally the smaller, or narrower the fret, the more likelihood of buzzing there is, and so for those guitars that do have very fine frets, it is usually necessary to curve the fret board back slightly, to increase the tightness of the strings against the frets.