God kept the manna from appearing on the sabbath day. Even though they had enough, some Israelites go out to gather more on the sabbath day despite God’s instruction for them to rest. Before the Law is even given, the people refuse to keep God’s instructions. God has given the people the sabbath and provided for them, and they still do not follow His instructions.
We often have in mind all that we need to do and fail to rest. Such is still, I think, dishonoring to God because He is still our provider and instructor. When we do not rest, we show that we believe ourselves to have to go and get. But, it is always the Lord who provides. He provides enough. I still believe that we should work six days a week and rest one. Rest does not mean doing nothing, but it does mean not gathering for ourselves as a matter of our regular labor. This may look different for each person or family.
Israel names this strange bread manna and keep some before the testimony throughout the generations. This is the first clue we receive that something was being kept so that Israel would remember what God has done. The testimony will later come to include the tablets of the Law and the Ark of the Covenant. I imagine that, at this time, it includes the story of Genesis and Exodus up to this point on Egyptian papyri (invented as early as the 4000s BC). Moses is a record-keeper, doubtless a trait he learned growing up as an Egyptian prince.