Mixing ratio is the mass of water vapor per unit mass of dry air in the same sample, usually reported in grams of water vapor per kilogram of dry air.
Why the ratio uses dry air
Dividing by the mass of the dry air rather than by the total mass of the sample has a useful property. The mass of the dry air in a closed parcel does not change as the parcel rises, sinks, or is compressed, so the mixing ratio does not change either as long as no condensation or evaporation occurs. This is what meteorologists mean when they say mixing ratio is conserved for unsaturated motion.
Saturation mixing ratio is a related quantity. It is the mixing ratio the air would have if it were saturated at its current temperature and pressure. Relative humidity, expressed as a ratio, is the actual mixing ratio divided by the saturation mixing ratio.
How forecasters use it
On a sounding, mixing ratio and saturation mixing ratio are plotted together to show how much moisture is present at each level and how close each level is to saturation. A deep column of high mixing ratio supports heavy rainfall and sustained updrafts because parcels lifted from any level in that column carry meaningful moisture upward.
Mixing ratio is also useful for tracking moisture across boundaries and through the diurnal cycle. Because it does not change with temperature, comparing morning and afternoon mixing ratios at the same site tells the forecaster whether real moisture has arrived or left, separate from any changes in relative humidity driven by heating alone.
Important limits
A single-level mixing ratio is only as representative as the sample. Near the surface, values can swing over short distances across a dryline or an outflow boundary, so one observation may not describe the airmass a few miles away.
Mixing ratio also does not tell you anything about instability, forcing, or storm mode. It only reports how much water vapor is present. Two environments with the same low-level mixing ratio can produce very different weather depending on the temperature profile, the cap, and the winds above.