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, conscious, aware of their surroundings, causing them to change and grow and function according to His design.
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 truthfully about our lives, understanding why we’re living as we are, identifying what sort of works we’re doing (1Co 3:13), and to stop doing things which are not energized by God, activities that are apart from and outside of Him, rooted in a carnal mind. (Ro 8:6)
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)
The difference between a living work and a dead work lies in the motive, and there’s only one proper motive: God is doing it. (Jn 5:19) Christ in us (Col 1:27) is living in our life (Col 3:4), breathing in our breath, willing through our wills, and doing through our doing (Php 2:13), as we actively seek to please and honor God with everything we have. (Col 3:17) When we’re living to please Him as deliberately as we know how, actively seeking His will and pleasure every moment, He is living through us and we’re abiding in Him. (Jn 17:21)
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 with thanksgiving (Col 3:17) for God’s glory. (1Co 10:31)