In this verse GOD is telling Moses how the nation of Israel will remember GOD bringing them to their own promised land, and out of slavery in Egypt. In Exodus 13:9 GOD says this remembrance must serve as a sign on their hand and memorial between their eyes in order that GOD's law may prove to be in their mouth.
The book of Revelation talks about the mark of the beast being on the hand and forehead. (Revelation 13:16; same chapter but in a different book.)
I was thinking if this could be about not practising religious observances and not exercising faith to remember GOD's law and thus not putting it in one's heart in the end times. Then the head and hands of those people will be honouring the ways of Satan instead of GOD. People could be looking at each other in hate or saying mean words instead of kind words. Hands could be being used to steal or push or hit other people instead of giving or hugging or shaking hands in friendship. Lawlessness will rule this time so as Revelation 13:17 says only people with this type of selfish behaviour will be able to succeed financially because money will be more important than justice or morality. Greedy people will control our financial infrastructure and in order to have more money a person will have to chose greed as well instead of honouring GOD's laws. Revelation 13:18 talks about the number 666. Nero was emperor at the time John wrote Revelation and in ancient time the Hebrew letters also represented numbers. Nero's name was also 666 with the number system prescribed to the letters in his name. Maybe this means that during the end times there will be a ruler who outspokenly denies GOD thus making it very popular to do so at the time, and making it impossible for those who honour GOD's laws to be financially prosperous because greed will determine success? Not taking the mark of the beast could be remembering GOD's goodness as a sign on their hand and memorial between their eyes in order that GOD's law may prove to be in their mouth.