What does 'agus beannacht Dé agat' mean?

In Irish it is common to hail people and say goodbye to them by invoking God's blessing on them. Hence there are a variety of sayings similar to the one queried. The phrase queried is not strictly accurate - it is a derivation of "agus beannacht Dé leat" which translates as "and God's blessing with you" which would commonly be said to a guest leaving your house. This should not be confused with "agus Beannact Dé ort" and God's blessing on you - this would be said as a thank you to some one who gave you something or did you a favour.
In keeping with the invocation of God's blessing the commonest form of greeting is "Dia dhuit" "God to you" said when meeting someone - the reply being "Dia 's Muire dhuit" "God and Mary to you". However etiquitte would require you to vary this if the person you were greeting was engaged in work. In such an instance the correct salutaion would be "Bail o Dhia ar an obair" "A blessing from God on the work".
For those who would not wish to make a reference to God the commonest greeting would be "Sé do bheatha" "Your health" NB plural is "Sé bhur mbeatha"