What m and M mean in chemistry?

The lowercase m (molality) refers to the concentration of a solution expressed as the number of moles of solute per kilogram of solvent. For example, a 0.1 molal solution of sodium hydroxide (NaOH) means there are 0.1 moles of NaOH dissolved in 1 kilogram of solvent (usually water). 

The uppercase M (molarity) refers to the concentration of a solution in terms of the number of moles of solute per liter of solution, not just solvent. For instance, a 0.1 molar (0.1 M) solution of NaOH contains 0.1 moles of NaOH dissolved in 1 liter of the solution, which includes both the solvent and the solute.