The water-cement ratio is the weight of the water in a concrete mix divided by the weight of the cement, and it's the single biggest factor in how strong and durable the concrete ends up.
When the mix includes fly ash or slag along with cement, it's called the water-cementitious materials ratio, written w/cm. It works the same way.
Here's the math. A mix with 564 pounds of cement per cubic yard (six 94-pound sacks) and a 0.50 ratio has 282 pounds of water, or about 34 gallons. Add 3 gallons a yard on site, about 25 pounds, and the ratio is 307 ÷ 564 = 0.54. The mix is weaker, and it'll shrink and crack more.
Lower ratios make denser paste with fewer connected pores, so water and salt have a harder time getting in. That's why codes and specs cap the ratio for concrete that will freeze, and cap it tighter where it sees deicing salt, usually at 0.45 or lower. The spec or local code sets the real limit for your job. Freeze-thaw protection also calls for air entrainment.
Lower isn't free. A drier mix is harder to place and finish, which is where water-reducing admixtures come in: they raise the slump without adding water. The ratio the plant designed is only the ratio you get if nobody adds water at the truck. See concrete slump for what's allowed on site.