In brief: A simple domicile mutual reception occurs when planet A occupies a sign ruled by B and planet B occupies a sign ruled by A.
A two-way sign relationship
Mars in Gemini and Mercury in Aries supply a straightforward example. Mercury rules Gemini, the sign occupied by Mars; Mars rules Aries, the sign occupied by Mercury. Each planet is in the other’s domicile. One can identify that reciprocal link from sign positions alone. It does not mean the planets are conjunct or otherwise aspecting; their actual angular separation must be calculated separately.
Why authors differ
The word reception has had wider technical meanings involving exaltation and other dignity rulers. Some horary authors also require an applying aspect before a reception can act in a judgment. A modern shorthand may call any two-way exchange of domicile signs mutual reception without that additional requirement. State which definition is used so two readers are not arguing over different tests under one label.
It is not automatically favorable
A reciprocal sign link may focus attention on a pair, but older sources also examine whether the planets are otherwise well placed. A reception rule is therefore not a promise that a relationship, project, or event will improve. Read the entire chart and the tradition’s criteria.
Check it step by step
First calculate both planets’ signs at a stated moment. Use a declared traditional or modern ruler mapping and make the two arrows explicit. Next check their actual aspect, houses, sect, and dignity if those are relevant to the question. With an unknown birth time, house claims should be left open; a planet close to a sign boundary may require a time-range test even for the basic two-arrow condition.