This passage is similar to others (e.g., Deuteronomy 6:6-9) throughout Moses' writings and concerns the preserving and propagating of the news of God's miraculous protection of the people of Israel and the marvelous legal code He had revealed to them. We can understand better the care by which this preservation was to take place, by noting the action verbs used in this passage.
First, the people were to "lay up" or impress the information in their hearts and souls. Every fiber of their being was to be aware of and in submission to the law. This personal commitment was to be aided by physical reminders "bound" on each person's hands and clothing, in plain sight, so that it could not be ignored or forgotten.
Next, the personal saturation was to move from the family leaders into the family, particularly the children. Parents were to "teach" the law, "speaking" of it at every opportunity, whether sitting, walking, lying down, or rising up. In this way, the personal would become corporate.
Finally, it was to become public, for each was instructed to "write" portions of the law where all could see and know of the personal commitment within.
Before God will give us a public ministry, there must be an inner submission to and love for the things of God. This should be obvious to everyone around us. Then God can use us at home and elsewhere to His glory. JDM