the ability to understand something instinctively, without the need for conscious reasoning.
intuition (n.) Look up intuition at Dictionary.com
mid-15c., from Late Latin intuitionem (nominative intuitio) "a looking at, consideration," noun of action from past participle stem of Latin intueri "look at, consider," from in- "at, on" (see in- (2)) + tueri "to look at, watch over" (see tuition).
intuit (v.) Look up intuit at Dictionary.com
1776, "to tutor," from Latin intuit-, past participle stem of intueri (see intuition). Meaning "to perceive directly without reasoning" is from 1840, in this sense perhaps a back-formation from intuition. Related: Intuited; intuiting.
intuitive (adj.) Look up intuitive at Dictionary.com
1640s, from Middle French intuitif or directly from Medieval Latin intuitivus, from intuit-, past participle stem of intueri "look at, consider" (see intuition). Related: Intuitively; intuitiveness.
teaching or instruction, especially of individual pupils or small groups.
tuition (n.) Look up tuition at Dictionary.com
mid-15c., "protection, care, custody," from Anglo-French tuycioun (late 13c.), from Old French tuicion "guardianship," from Latin tuitionem (nominative tuitio) "a looking after, defense, guardianship," from tuitus, past participle of tueri "to look after" (see tutor). Meaning "action or business of teaching pupils" is recorded from 1580s. The meaning "money paid for instruction" (1828) is probably short for tuition fees, in which tuition refers to the act of teaching and instruction.