AT that time, Jesus entered into a certain town: and a certain woman named Martha, received Him into her house. And she had a sister called Mary, who sitting also at the Lord's feet, heard his word. But Martha was busy about much serving. Who stood and said: Lord, hast thou no care that my sister hath left me alone to serve? speak to her therefore, that she help me. And the Lord answering, said to her: Martha, Martha, thou art full of care, and art troubled about many things: But one thing is necessary. Mary hath chosen the best part, which shall not be taken away from her.
This Gospel was received, like the feast of the Assumption itself, from the Byzantine tradition, in which it is read on various feasts of the Blessed Virgin, with two verses from the following chapter appended to it. (Luke 11, 27-28) In the traditional lectionary of the Roman Rite, these two verses are separated from the previous Gospel, and read on the Vigil of the Assumption.
AND it came to pass, as He spoke these things, a certain woman from the crowd, lifting up her voice, said to Him: Blessed is the womb that bore thee, and the paps that gave thee suck. But He said: Yea rather, blessed are they who hear the word of God, and keep it.
The highly influential medieval liturgical commentator William Durandus explains allegorically why this Gospel is read on the Assumption:
The Gospel is read about Martha and Mary, which at first sight appears to have no relevance, and yet it is indeed relevant, according to an allegory. For Jesus entered into a certain ‘small castle’, that is, into the Virgin Mary, who is called a castle since She is terrible to demons, and armed Herself well against the devil and against vices. But She is called ‘a small castle’ in the diminutive (castellum) because of her humility, and because of Her unique condition, since “neither before nor henceforth hath there been or shall be such another.” (quoting the 2nd antiphon of Lauds on Christmas day.) And Martha, that is, the active life, received Him. For She most diligently reared Her Child, and brought him into Egypt, and showed her goodness in the active life, by going to Elizabeth, and serving her, and just as She was (like) Martha in the active life, so also she was (like) Mary Magdalene in the contemplative life. Whence in another Gospel is read, “Mary kept all these words in her heart.” (Luke 2, 50) Now these two sisters signify the active life and the contemplative life, which were clearly in the Blessed Virgin Mary, and through them she exaltedly, honorably, and with great delight, received Christ in Herself. (Rationale Divinorum Officium, Book 7, chapter 24.)
The Dormition and Assumption of the Virgin Mary, by Don Silvestro dei Gherarducci; from the Gradual of Santa Maria degli Angeli, ca. 1370, now in the British Library.