Ordinals is short for Ordinal Numbers, or Ordinal Theory, which in the context of bitcoin was created by Casey Rodarmor. Casey theorized and developed a methodology to sequence individual satoshi’s and assign them a non-fungible designation, along with an application to track and identify their assigned value.
When this ordinal theory is combined with an inscription process allowed via the taproot upgrade and segwit discount, people can ascribe a perceived association between the inscription and an individual satoshi’s ordinal designation to create a non-fungible like quality.
Casey’s ordinal theory methodology is just one of many types that can be applied, but is the primary methodology referred to when people say “ordinals”