The Latin word introspicere means to look inside, and that's what an introspective person does, metaphorically speaking.
What is the root of introspective?
introspection (n.)
1670s, "action of closely inspecting or examining," noun of action from past participle stem of Latin introspicere "to look into, look at, examine, observe attentively," from intro- "inward" (see intro-) + specere "to look at" (from PIE root *spek- "to observe").
Who created introspection?
Wundt's Psychological Research
Wundt believed that there were two key components that make up the contents of the human mind: sensations and feelings. Wundt focused on making the introspection process as structured and precise as possible.