Rabbi Julian Sinclairs dip into the dictionary
Shiur has two common uses. In the first, it means a class or lecture on any Torah subject. Shiurim may be about Talmud, the weekly parashah, chasidism, mysticism or any other area rooted in traditional Jewish sources.
The word literally means a quantity, measure or amount, deriving from shaar, meaning gate, that is, an opening of a certain size. So shiur in this first meaning just means an amount or chunk of Torah.
The second meaning is more literal. In this sense a shiur is the precise amount or measurement of material that is necessary for defining whether a mitzvah has been done or a prohibition transgressed. So, there is a minimum shiur of matzah to be eaten in order to fulfil the mitzvah of eating matzah on Seder night, a kazayit (that is an olives volume, though olives in the time of the Talmud seem to have been larger than those of today).
There is a minimum shiur of distance for violating the prohibition against carrying in the public domain on Shabbat (four cubits, about six feet) and minimum shiurim for the amount of a substance that we need to carry in order to have violated that prohibition. (These depend on the type of substance or object in question.)
Across the whole range of Jewish law, there are shiurim determining when and how we infuse the physical world with holiness through doing mitzvot.