The meaning of "to seek" in the Bible is pretty straightforward, but there is a bit of nuance. In most cases "seek" or "look for" is connected with truth and knowledge, where "desire" is connected with love and affection. This makes sense; the idea of "seeking" is connected to sight, and sight corresponds to our intellect and capacity to understand truth.

(Odkazy: Apocalypse Explained 550; Apocalypse Revealed 429; Arcana Coelestia 4719, 6770, 6771, 7021, 8298)

429. In those days men will seek death and will not find it; they will desire to die, and death will flee from them. (9:6) This symbolically means that those people caught up in the doctrine of faith alone wish the intellect to be closed and the will stopped up in matters of faith, and thus that they be without any spiritual light and life; but that still the Lord has provided that the intellect be not closed or the will stopped up, to keep the spiritual light and life in a person from being extinguished.

"In those days" symbolizes the last state of the church, when the doctrine of faith alone has been universally accepted. "Men will seek death" means, symbolically, that they wish the intellect to be closed in matters of faith. "And will not find it" means, symbolically, that the Lord has provided that this not happen. "They will desire to die" means, symbolically, that they also wish the will in them to be stopped up. "And death will flee from them" means, symbolically, that the Lord has provided that this not happen either. For in that case spiritual light and life would be extinguished, and the person would spiritually die. Seeking is said in application to the intellect, and desiring to the will, and death is said in application to both.

It is apparent that this is the symbolic meaning of these words. Otherwise what would it mean that men in those days will seek death and not find it, or desire to die and have death flee from them? For the only death meant by death here is spiritual death, which is induced when the intellect is banished from tenets to be believed; for a person then does not know whether he is thinking and putting into practice truth or falsity, thus whether he is thinking and acting in concert with angels in heaven or in concert with devils in hell.