Primitive: From "primus" = "first": What comes first. In logic, primitive terms are terms such as one must presuppose as (mostly) understood in order to set up a certain theory.
Since all reasoning must start with some assumptions, there are bound to be some primitives, though of course one can set up different theories with different primitives that explain (parts of) the same domain and thus help to clarify the primitives in one theory in terms of those in the other.
Also, it is noteworthy that the prior understanding of a primitive term that one has from natural language in a formal language normally gets somewhat sharpened, more precise and partially distinct from the meaning and usage of the term in natural language.
In propositional logic, the standard primitives are and, or and not, sometimes extended to included if-then and iff (if and only if), or restricted to just and and not, or or and not, or the Sheffer-stroke that's defined in terms of not both.
In predicate logic, standard primitives are one or both of the quantifiers and sometimes identity, next to predicates and subjects. In set theory the standard primitive is element.