Dead things are missing that life force from God, the energy and vitality He gives to all living things (Ac 17:25), making them sentient, aware of their surroundings, causing them to change and grow and function as they ought.
To repent is to start believing the truth about something, and to start acting differently as a result. (2Ti 2:25-26)
So, repentance from dead works must be to start thinking differently about our lives, understanding why we’re living as we are, identifying what sort of works we’re doing, and to stop doing things which are not energized by God, activities that are apart from and outside of Him.
Christ says that unless we’re abiding in Him, we can do nothing that’s worth doing (Jn 15:5); unless we’re aligned with Him, seeking to honor and obey Him, we’re working against Him. (Mt 12:30) In other words, if we’re willing to continue living our lives apart from Him, out of fellowship with Him, for our own pleasure, then we’re the walking dead (1Ti 5:6), having only the outward appearance of life (Re 3:1): we’ve yet to begin the spiritual life. (Ep 2:1)
Everything we do, we choose to do; to repent of dead works is to start making different choices, in every choice we make. It’s a fundamental life change, a transformation, living for a different reason than we’ve been living, living for God instead of for ourselves.
If there’s something we’re thinking that Christ can’t be thinking, that He would find distasteful or repugnant, let’s stop thinking that; if we’re going where Christ wouldn’t go, let’s stop going there; if we’re speaking words He wouldn’t speak, let’s stop speaking them. Let’s be thinking what Christ in us is thinking, doing what He’s doing, and going where He’s going. If Christ dwells in us, let’s let Him live as He will in us, incarnating Himself again in this evil world through us. Everything we do, let’s do it in Christ’s name (Col 3:17) and for God’s glory. (1Co 10:31)