Shepherds were a despised group of people amongst God-fearing Jews. However much they tried, they could never have kept the details of the ceremonial part of the Law. What we miss from a cursory reading of this perhaps over-familiar Bible passage is that these shepherds were keeping their flocks on the hills around Bethlehem and this is where the Temple authorities were known to keep their flocks. From these sheep the Temple offerings would have been chosen. Therefore, the outcast shepherds who tended the Temple lambs, keeping them for slaughter, were the first people to see the Lamb of God who takes away the sin of the world.
A couple more things we can learn from these verses:
1. The Angels came to the shepherds when they were going about their normal work routines. They almost certainly hadn't spent days and nights calling on God to come: they hadn't been, as in many charismatic meetings, 'welcoming' the Holy Spirit. God came amongst them, He CHOSE them, it wasn't anything which they had done or said or not done or said that brought Him near. God is Sovereign and He does whatever He chooses. He is not our puppy, nor a cosmic slot machine. Whilst earnestly looking for revival, we can so easily miss the real work of God going on.
2. The way that Jesus was born was a marker for the shepherds, because of it being unusual. Yes, we may feel upset that Christ came into the world in such a fashion, but this is one of the ways in which He stood out. At times in His growing-up and all the time in His ministry, Jesus stood out!