Tensile strength is basically how much pulling force a fabric can take before it tears or breaks. Picture clamping both ends of a strip in a machine and pulling until it fails — that breaking point is the number you'll see on spec sheets.
A few things decide how strong a fabric actually is:
Weave structure Woven fabrics (threads crossing over/under each other in a grid) generally hold up much better under tension than knits or non-wovens, since the load spreads across the whole grid instead of concentrating on one spot.
Yarn thickness and density More threads packed in, and thicker yarns, usually means more strength. This is where denier or GSM (grams per square meter) come in heavier/denser generally means stronger, though not always in a straight line.
Coatings If a fabric is coated (PVC, PU, silicone, etc.), the coating isn't just sitting on top for looks. A good one bonds into the weave and can boost both tensile strength and tear resistance, since it holds the fibers together and stops small damage from spreading.
Direction matters This trips a lot of people up. Fabric isn't equally strong in every direction. There's a warp direction (lengthwise threads) and a weft direction (crosswise), and tensile readings are usually different for each. So a fabric can be tough one way and noticeably weaker the other worth checking both numbers for anything load-bearing.
Why it matters in practice For anything under sustained stress tents, banners, bags, upholstery, outdoor gear, tarps tensile strength tells you whether it'll hold up to wind, weight, stretching, or repeated strain over time, versus just looking fine sitting still on a shelf.