Gospel wakefulness means treasuring Christ more greatly and savoring his power more sweetly. Treasuring Christ more greatly and savoring his power more sweetly is simply the the long way of writing worship.
Worship is the ascribing of the worth to something or someone. In this case, of course, the recipient of this worship is God, the only one worthy of our worship. What happens in gospel wakefulness is that in our brokenness, our sense of self-worth and sufficiency in things other than God gets destroyed, and as the good news of Christ's finished work is applied to us, our affections become reformed, renewed, and revitalized.
Jared Wilson in Gospel Wakefulness, p 77 (bold emphasis mine).