The poem Virtue by George Herbert is set out in four four-line stanzas in the first three of which he selects an typical image of beauty and life (the day, a rose, the spring) before reminding us that the image "must die".
The final stanza from which this metaphor comes focuses on the "sweet and virtuous soul". Herbert procedes to state that the soul alone will "never give" and will continue to "live" immortally whilst the world around it rots and decays.
The specific image "turn to coal" is a reference to the decay of the physical and material world: coal is the byproduct of the rotting of vegetable stuff. Coal is also particularly apt as a contrast to the "seasoned timber" to which the soul is compared in the preceding line: timber is useful and living; coal is dead and rotted.