In Genesis, the "Tree of Life" is a tree that grants immortality—God prevents humans from eating from it after they fall, so that they won't become both immortal and yet trapped in a fallen state (apparently).
In Proverbs, this immortality-granting tree is used as a metaphor for wisdom and for any really good qualities a human being might have:
She [Wisdom] is a tree of life to them that lay hold upon her: and happy is every one that retaineth her. (Proverbs 3:18)
Another saying gives a good example of how Proverbs tends to apply the image: "Hope deferred makes the heart sick, but a desire fulfilled is a tree of life" (Proverbs 13:12). Wisdom and a fulfilled desire are both "trees of life" because they pull human beings back from courting their own mortality. Wisdom prolongs life and makes it enjoyable, and a fulfilled desire makes life pleasant instead of a long, frustrating slog.
In a higher sense, Proverbs is recommending Wisdom as a method for recovering from the Fall. It helps shake off the deleterious effects of eating from the Tree of Good and Evil, and leads the person who loves Wisdom towards more life.