A market maker quotes both a bid and an ask, capturing the spread on round-trip trades. The basic edge is the spread; the basic risks are inventory and adverse selection.
Inventory risk is exposure to price moves while holding non-zero position. Market makers manage it by skewing quotes — when long, lower both bid and ask to encourage selling and discourage buying.
Adverse selection is the risk that the counterparty knows something you don't. If informed flow systematically picks off your stale quotes, you lose money on every trade. Market makers update quotes quickly when the market moves and pull quotes during news events.
The textbook Avellaneda-Stoikov model formalizes optimal quoting as a stochastic-control problem: solve for bid/ask offsets that maximize expected utility given inventory aversion and arrival intensities. Practical systems layer on dozens of adjustments for risk limits, latency, and microstructure.