What do quantitative and qualitative measurements mean in science?

Quantitative means measuring a quantity - putting a value to something. For example, you might measure the rate of a reaction by seeing how many seconds it takes for a change to happen, such as a piece of magnesium ribbon to dissolve in acids of different concentrations.

Qualitative means without determining a value. You might simply be doing a comparison, e.g. the magnesium dissolves more quickly in this acid than in that one, or making observations: lithium produce a red flame colour while sodium compounds produce a yellow one.