‘The churches of Asia salute you. Aquila and Prisca salute you much in the Lord, with the church that is in their house. All the brethren salute you. Salute one another with a holy kiss.'
He then adds the salutations of the other churches, so that they might feel a oneness with them. All the churches were to see themselves as one. This includes especially the church in the house of Aquila and Prisca (Priscilla) for these two were well known to them (Acts 18:2). He wants them to know that their hearts are with them still (‘salute you much in the Lord'). ‘All the brethren' probably signifies all Paul's helpers, for the churches have already been mentioned.
Aquila and Priscilla were clearly wealthy enough to own a house large enough to act as a gathering place for Christians. Aquila, like Paul, was a tent-maker (Acts 18:2-3). The unusual placing of Priscilla first in Acts 18:26; Romans 16:3 may suggest that their earthly wealth and status came from her side, Luke correctly acknowledging her status in his description.
‘Salute one another with a holy kiss.' While hearing the salutations of others they are to also salute each other in the conventional way, with a holy kiss (he may have in mind that there may have been kissing among them which was not really holy). Such a kiss was a recognised part of worship among the early church. Thus the reading of his letter is to be a cause of mutual salutation and awareness of the salutations of all the churches, a recognition of fellowship between all.
(It is regularly a problem to know when Paul is the innovator, and when he simply describes what was the custom in the churches, for his is often the first mention we have of what were later certainly customs within the church, as revealed for example in the Didache).