An anvil is the broad, flattened cloud that spreads out near the top of a mature thunderstorm where the rising updraft can no longer push higher and is forced sideways by upper-level winds. The classic shape resembles a blacksmith's anvil, wide at the top and narrower where it joins the updraft column below.
How the anvil forms
A thunderstorm updraft rises as long as the parcel inside it is warmer and less dense than the air around it. When the updraft reaches the tropopause, a stable layer where temperature stops falling with height, the parcel loses its buoyancy and cannot climb any further under its own power. The cloud material spreads horizontally instead of vertically, guided by the strong winds that typically live at that altitude.
The anvil is made almost entirely of ice crystals, because the temperature at the tropopause is well below freezing. Those ice crystals can be carried a long way downwind before they settle out, which is why mature storms fan out a long plume of cirrus in the direction of the upper-level flow.
How spotters and forecasters read it
A hard, sharply defined anvil edge points to an updraft that is still lifting fresh cloud material fast enough to keep the edge crisp. A fuzzy, wispy, or dissipating edge points to an updraft that is weakening and letting the anvil age. Chasers use the direction the anvil spreads to identify where upper-level steering is taking the storm.
Two anvil variants carry extra meaning. A dome that rises above the flat anvil is an overshooting top and indicates that the updraft has enough momentum to briefly punch through its equilibrium level. An anvil that spreads upwind against the upper flow is back-sheared and points to a particularly strong updraft.
What the anvil does not tell you
Anvil coverage on satellite can lag storm intensity by a long time. Cirrus that was produced by a strong updraft a half hour ago can still shade the ground long after the updraft that made it has weakened. Judging current storm strength from anvil area alone is easy to get wrong.
The anvil also shades and destabilizes air well downstream of the parent storm, which can complicate forecasting new development. When reading the sky, pair anvil appearance with the base of the storm and with radar, not with anvil alone.