In more detail
Molarity is moles of solute / litres of solution, and moles come from mass divided by Molecular weight. The volume is that of the finished solution, not of the water added: the solute is dissolved and then topped up to the mark in a volumetric flask. Smaller units are millimolar (mM) and micromolar (µM). Dilutions follow C₁V₁ = C₂V₂. Because liquids expand with temperature, molarity shifts slightly when a solution warms; molality, in moles per kilogram of solvent, does not.
Why it matters
Lab recipes, buffers and reagent concentrations are written in molarity, so mistakes multiply through an experiment. Dissolving a solute in a full litre of water gives more than a litre of solution and a lower concentration than intended, and confusing mM with µM is a thousandfold error.
Example
10 g NaCl (58.44 g/mol) = 0.1711 mol; made up to 0.5 L → 0.342 M
250 mL of 0.1 M NaCl needs 0.1 × 0.25 = 0.025 mol × 58.44 = 1.461 g
Normal saline, 0.9 % (9 g/L): 9 / 58.44 = 0.154 M
50 mL of 2 M made up to 200 mL: 2 × 50 / 200 = 0.5 M