Degen is a contraction of "degenerate gambler," adopted as a self-identifier by high-risk cryptocurrency speculators who engage in aggressive trading with full awareness of — and general indifference to — the probability of loss. The term is used without the shame its dictionary definition implies; within the community, being a degen is a statement of risk tolerance and trading philosophy, not an admission of pathology.
Usage
Degen functions as both a noun ("he's a degen") and an adjective ("that's a degen trade"). As a noun it describes a person; as an adjective it characterizes a strategy that prioritizes potential upside over risk management. "Degenning into something" means buying aggressively without doing extensive research.
The term is often used affectionately within the community. Being called a degen by another degen is not an insult. The insult version is "smoothbrain degen" or similar, which implies the person lacks even the self-awareness that usually accompanies degen behavior.
The degen calculus
Degen traders typically reason differently from conventional investors. Rather than calculating risk-adjusted expected returns, degens often think in terms of asymmetric lottery tickets: what is the maximum upside if this works, and can I afford to lose the entry? If the answer is "100x possible, I can afford to lose this," the trade is often taken regardless of probability.