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.

288. That 'man' (homo) is used to mean the member (vir) of the Most Ancient Church, that is, celestial man, has been shown already indeed that the Lord alone was Man, and that from Him every celestial man was Man because he was His likeness. Consequently everyone who belonged to the Church, no matter who and without exception, was called man (homo). And in the end anyone who in body looked like a human being was called man to distinguish him from animals.