This remark was made by Jesus when he visited the home of Mary and Martha. Martha was distracted with preparing the meal and other household necessities; while Mary seemed intent on listening to Jesus' words. Martha complained that Mary was neglecting her household responsibilities; but Jesus emphasized to her the importance of listening to his words. The meaning is, of course, that daily household preparations are temporary and have no lasting significance, but the words of Jesus would have a far more lasting and meaningful effect than day to day chores. Jesus seemed to emphasize the importance of his teachings at another point when he said:
Heaven and earth shall pass away; but my words shall not pass away.
The Prophet Isaiah said,
The grass withers, the flower fades, but the word of our God stands forever.
So, by saying that Mary had chosen the best part; Jesus meant that she had made the wiser choice. One might even say that she had exercised the better part of discretion.