AC analysis
Many circuits treat different frequencies very differently, a filter passes bass and blocks treble, an amplifier loses gain at high frequencies. AC analysis maps that out: it asks, for a tiny wiggling signal, how much does the output grow or shrink and how much does it lag, at every frequency across a range. The result is the frequency response, usually drawn as a Bode plot.
The trick is that AC analysis is a small-signal, linear analysis. SPICE first finds the DC operating point, then replaces every device with its slope (its small-signal model) at that point, and computes the response to an imagined tiny sine wave. Because it is linearized, the input amplitude is irrelevant, it reports a ratio (gain) and a phase shift, not absolute volts, and it cannot show clipping or distortion. The command, like '.ac dec 100 1 1Meg', sweeps frequency (here 1 Hz to 1 MHz, 100 points per decade). Capacitive reactance falls with frequency as 1/(2 times pi times f times C), which is exactly why a high-pass filter's gain climbs and then levels off.
AC analysis is how you read a filter's cutoff frequency, an amplifier's bandwidth and gain-bandwidth product, and, crucially, its phase margin, the warning sign of whether a feedback loop will be stable or break into oscillation. But remember its linear nature: it tells you nothing about large swings hitting the supply rails or slew-rate limits. For those you need a transient run.
AC-analyzing a simple RC low-pass with R = 1.6 kilohm and C = 100 nF shows flat gain at low frequency, a knee near f = 1/(2 times pi times R times C) which is about 1 kHz, then a steady fall of 20 dB per decade, the textbook single-pole roll-off.
Gain and phase versus frequency: the Bode plot that reveals bandwidth, cutoff, and stability margins.
AC analysis is linearized around the bias point, so it never shows clipping, slew limiting, or distortion. A result that looks fine here can still misbehave on big signals, which only a transient run reveals.