How do batteries and electric vehicles (EVs) contribute to grid stability as market assets?

They are flexible storage: a battery absorbs surplus and releases it later (arbitrage, demand response), and EVs do the same as mobile batteries through smart charging.

The grid's core problem is that supply and demand rarely match instant to instant. Storage assets buy time:

• Battery — a decentralized storage device that stores surplus/cheap energy and discharges it when needed. This enables demand response (shifting load in time), energy arbitrage (store low, use or sell high), and smoothing of the imbalance.
• Electric vehicles (EVs) — mobile energy assets equipped with batteries; through smart charging they can charge when there is surplus and, in principle, feed back when there is scarcity.

Both let the market shift energy across time rather than having to consume it the instant it is produced — which is what makes intermittent renewables manageable.

Go deeper:

• Vehicle-to-grid (Wikipedia) — How plug-in EVs feed stored energy back to the grid as demand-response assets.
• Demand response (Wikipedia) — Shifting consumption in time to match supply — the flexibility storage provides.