Most tennis racquets are what we call two string design employing a single vertical and a horizontal string
.
It is normal at a restring to have the same tension applied to each string and normally guidance on this is given on instructions printed on the racquet frame.
Basically the tighter the string the better the control and the lower the tension the more power is developed.
However there is a drawback to a conventional two string racquet that results in the playing causing string side to side movement and eventual notching , usually of the main string (the vertical). The racquet strings then start to lose tension and eventually snap, usually when you are playing that important point of the game and out comes the spare racquet.
Deciding when the right time has come to restring is not easy and is usually decided on your budget and your playing level. You will often see professional players change a racquet after 8-12 games and off runs their stringer to freshly restring a new weapon, usually to arrive back as the game is over but that is the way things seem to happen.
Then the budget player leaves the strings till they break and he of course then depends on having a second racquet or a generous tennis buddy to lend him one of theirs.
There are however rather unique racquets that feature 3 strings known as Mad Raq racquets and these are the world's only three string racquets whereby the string lasts almost indefinitely due to the complete lack of string see sawing and notching.
These racquets hold their tension longer and therefore the ball response stays constant.
The thickness of string is called the gauge and these vary from 1.2 mm to about 1,4 mm, anything above that is for cranes not for tennis racquets and the types of string vary a lot also. Natural gut was a big favourite years ago made from pigs bladders, sounds awful but thats what they were. Then synthetic gut came along and gave a somewhat similar feel and had the advantage that it was waterproof which natural gut was not.
Then the Nylons and synthetics came along in multitudes, with massive price and quality variations. These days it is possible to transform any racquet with the right or wrong string choice. Irradiated strings are a good bet as they are processed such that they do not stretch as much as most strings and hold tension well.