Why is atomic mass important for the student to understand?

Atomic mass is extremely important in chemistry because it is the connection between mass, which we can measure in the laboratory, and moles, which are numbers of atoms. Most of what we study in chemistry is determined by ratios of atoms. The atoms react in fixed and definite proportions; for example, sodium and chlorine atoms combine in a one-to-one ratio to form sodium chloride. Chemical formulas also have fixed ratios. Water is H2O, meaning a combination of two hydrogen atoms and one oxygen atom.
Because the atomic masses of the different elements are different, we cannot "see" the ratios in which atoms react and combine just by looking at mass. To get into the “world” of chemical formulas and chemical reactions, we always want to convert to moles. A mole of any kind of atom is a specific number of that kind of atom, so if one sodium atom combines with one chlorine atom to make sodium chloride, then one mole of sodium atoms will combine with one mole of chlorine atoms to make sodium chloride. In terms of mass, 22.99 g of sodium combines with 35.45 g of chlorine. We cannot see the simple one-to-one ratio just by looking at mass.
However, we need moles for more than just understanding the simple ratios in which elements combine. We can find the empirical formula of an unknown compound by converting the masses of all of the elements in the compound to moles and then by finding the ratios of the elements. We also need to use moles when predicting how much product will be produced in a chemical reaction or when determining how much starting material is needed to make a desired amount of some chemical. Atomic masses and formula masses for compounds, which are found from atomic masses, are the key to converting into this world of moles where all of chemistry takes place. When the atomic comparisons are finished, atomic masses are the key to converting back to grams to predict how much of something we will be able to measure on a balance in the lab.
Being able to correctly use atomic masses to find formula masses and convert back and forth between grams and moles is one of the most essential skills in chemistry. It is pretty important to be able to understand and use atomic masses.