Walking represents living, and usually means living according to the true things taught to us by the Lord -- to "walk in His ways." When the Lord is pictured walking, it means life itself.

2508. 'She is my sister' means rational truth. This is clear from the meaning of 'a sister' as rational intellectual truth, dealt with in 1495. That rational truth is meant by 'a sister' cannot be seen by anyone except from the heavenly marriage; for the things that descend from that marriage have links with one another - resembling the ties of blood-relationships and relationships by marriage on earth, concerning which see 685, 917 - and in ways endlessly varying. The heavenly marriage exists solely between Divine Good and Divine Truth. Conceived from that marriage there exist with man the capacities to understand, to be rational, and to have knowledge; for without this conception from the heavenly marriage no one can possibly be endowed with understanding, reason, or knowledge, and cannot consequently be a human being. Insofar therefore as he draws from the heavenly marriage he is human. The heavenly marriage exists within the Lord Himself, so that the Lord is that marriage itself; for He is Divine Good itself and at the same time Divine Truth. The heavenly marriage exists with angels and men insofar as love to the Lord and charity towards the neighbour, and consequently insofar as faith derived from these exist with them, that is, insofar as the Lord's good and the truth derived from this do so. When this is the case with them they are called 'daughters and sons', and in relation to one another 'sisters and brothers', but with differences. The reason rational truth is called 'a sister' is that it is conceived from the influx of Divine Good into the affection for rational truths. The good conceived in this way in the rational is called 'a brother', and the truth 'a sister'. But this will be clearer from the words spoken by Abraham in verse 12 of this chapter, 'And also she is truly my sister, my father's daughter but not my mother's daughter; and she became my wife'.