These things don't have to be 'smallest' or 'largest'. They are simply (what especially high-energy physicists would agree to be) the most natural units in which to carry out calculations when doing fundamental research. The crux is realizing that things like a 'second' and a 'meter' or a 'kilogram' are purely invented because they are convenient in everyday life situations for humans. This nice convention is, however, ridiculous when you're working with very tiny or maybe very large things.
Therefore, the question naturally arises: "What can we use as units to measure physical quantities, independent of our (essentially) arbitrary vantage point as humans?"
The answer is: use the units that you find to be unity when you set all fundamental natural constants to unity. Thus, the prescription for finding natural units is: set all fundamental constants to 1, and rearrange them in different ways to get all kinds of derived units. This does not say anything about whether they are the smallest, largest, or whatever-est quantity.
EDIT: the link in Qmechanic's comment has a nice explanation by Ron Maimon on the particular case of the Plank mass.