One of the most important characteristics of any spun yarn is its breaking strength: how much tensile stress it can bear before, well, breaking. A yarn's strength will determine it's processability as well as the longevity of any garments made from it.
Typically, yarn strength is measured two ways:
1) Tensile strength testing
2) Lea strength testing
A test of raw tensile strength is done by simply clamping a length of yarn at both ends and stretching it until it breaks (usually this is done to several samples of a given yarn with a average taken, to compensate for the possibility of a given length being abnormally strong or weak). Lea strength testing (which has largely become the industry standard) is done by spooling 120 yards of yarn on a wrapping reel and then feeding that spool into a specialized testing machine with jaws that snag, twist and yank the fiber.
Yarn's performance in terms of its lea strength is measured as its 'count strength product' or CSP. The industry standard is that commercial grade yarns must have a CSP of higher than 1800, while yarns scoring above 2200 are of exceptionally good quality.
You can check the (rough) CSP of the yarn you're buying in a slightly less scientific way via either it's hairiness or its elasticity:
If you try and stretch a length of yarn and it has very little elasticity, odds are it will also have a lower CSP. Likewise, if a yarn is very 'hairy' (lots of little loose strands hanging from it), odds are the CSP is fairly poor.
Stronger yarns make garments that last longer... though sometimes the trade-off for really high CSP is that natural fibers must be blended with acrylic fibers.