String tension refers to how tightly the strings on an instrument are wound when tuned to pitch. Generally, the larger the gauge of the string, the tighter it will have to be wound to reach a certain pitch – for example, a .048″ wound string will have to be wound tighter to reach a Low G note, at a 25 inch scale length, than a .042″ string would.
Each gauge of string has an ideal tension range at which it performs best, and this range can vary depending on what the string is made from, and how it is made. The actual pitch that a string can be tuned to within the range of its ideal tension will vary depending on the scale length of the instrument. For example, a .042″ string might work well for a middle G pitch on a mandolin, while on an acoustic guitar it might work well for Low G – a full octave lower than the same string would be on the mandolin.
The best way to figure out what gauge string to use for a particular intended pitch on an instrument is to find a comparable “standard” instrument in a similar scale length. For example, if you want to tune to Low A on your cigar box guitar that has a scale of 24 inches, you could look at a standard acoustic guitar string pack, since an acoustic guitar has a string tuned to Low A. You could probably use that same gauge string as either Low G or Low B, which are the notes on either side of A. There is generally some wiggle room on either side of what a particular string gauge can be used for, and close enough is often good enough.
A general rule of thumb is this: if a string seems too loose and flappy/buzzy at your intended pitch, go with a larger gauge string. If it is too tight or breaks, go with a smaller gauge string.