A relationship is the state of being related or connected — between people, between groups, or between things — and, in its most common modern use, an ongoing romantic or sexual connection between two people.
The word spans three ranges built on one skeleton. There is kinship and descent, the sense in which two people are related by blood or marriage. There is correlation, the sense in which any two variables have a relationship: price and demand, sleep and mood. And there is the interpersonal, the sustained pattern of dealings between people, whether commercial, diplomatic, or intimate. Only the third is ordinarily meant when the word stands alone, and that narrowing is recent — the specifically romantic or sexual sense dates to 1944, well after the word itself.
Relationship is a 1640s formation, relation plus the suffix -ship, which names a state or condition as it does in friendship and kinship. Relation itself reaches English around 1300 meaning "connection, correspondence," from Latin relationem, "a bringing back, a report," from referre, "to carry back." The literal reading — the condition of being related — is loose enough to explain how one word stretched from genealogy to statistics to romance without ever needing a second word.
Modern usage keeps a soft division between the two forms: relation handles kin and abstract or logical links, relationship handles the interpersonal. The near-neighbor worth separating is 📝connection, which names the link itself and can be momentary; a relationship implies duration, repetition, and mutual expectation.
Two definitions I keep: "a great relationship is about two things first, find out the similarities, Second, respect the differences" and "a true relationship is two unperfect people refusing to give up on each other."