What is a biblical commandment? I understand there are the ten commandments, which I naively presumed were the only "commandments" in the bible. I am under the impression that this is not true and that there are additional commandments. If this is true, what defines an instruction as a commandment in the bible?
A Biblical commandment as applied to scripture is a directive from God to a people group. In the Old Testament, this was always from God the Father and was always directed to Israel by way of the Prophets. Most of the commandments are found in the Pentateuch, although God spoke through other prophets during different times in Israel's history.

In the New Testament, commandments came from the Messiah directly and were directed to Christian believers. The Apostles did not add to the commandments of Messiah but referred to Messianic commandments in their writings to the churches. 

Any other commandments found in scripture would not be considered Biblical commandments but instead represent historical commandments from humans to other humans.