After hearing Simeon's words at the temple, Joseph and Mary marveled at the things which were spoken about Jesus. Although they had been prepared by the previous revelations concerning the destiny of this new Baby, the reality of the situation had not fully sunk in yet. And, although they don't realize it yet, raising the Messiah as their Son would have its challenges and sorrows, as Simeon alludes to in the next verses.
"Then Simeon blessed them, and said to Mary His mother, 'Behold, this Child is destined for the fall and rising of many in Israel, and for a sign which will be spoken against (yes, a sword will pierce through your own soul also), that the thoughts of many hearts may be revealed'" (Luke 2:34,35).
What did Simeon mean: "This Child is destined for the fall and rising of many"? To some Jesus would be a stone of stumbling and to others He would be a precious cornerstone (cf. I Pet. 2:7,8; Acts 4:11; Romans 9:32,33; Isaiah 8:14,15). Jesus would be spoken against and encounter much opposition (in His early life via Herod, throughout His ministry, and perhaps most noticeably during His arrest, trial, and crucifixion; cf. John 1:11). The crucifixion of Christ would be like a sword piercing Mary's soul. Her sorrow would be very intense as His mother, and even more so perhaps for lack of understanding why (cf. John 19:25-27). When Simeon stated that "the thoughts of many hearts may be revealed", I believe the idea here is that the true attitude (or heart) of every person who becomes knowledgeable of Christ's crucifixion is always shown in their response (or lack thereof) to the gospel.
"Now there was one, Anna, a prophetess, the daughter of Phanuel, of the tribe of Asher. She was of a great age, and had lived with a husband seven years from her virginity; and this woman was a widow of about eighty-four years, who did not depart from the temple, but served God with fastings and prayers night and day. And coming in that instant she gave thanks to the Lord, and spoke of Him to all those who looked for redemption in Jerusalem" (Luke 2:36-38).
Anna is described as a "prophetess," though we know nothing of her work as such. It is unclear as to whether she had been a widow for 84 years or whether she was a widow who was now 84 years old. Most likely, the latter is the correct understanding. Anna spent her time in the temple serving God "with fastings and prayers." Her words are not recorded, but she too spoke concerning the "Hope of Israel" and gave thanks to God!
"So when they had performed all things according to the law of the Lord, they returned to Galilee, to their own city, Nazareth" (Luke 2:39; cf. Matt. 2:22,23). Mary and Joseph did eventually return to Galilee, but Luke omits to record that they returned to Nazareth by way of Bethlehem and Egypt, according to Matthew's account.