The biquad~ object is a biquadratic filter. In technical terms, that’s a second-order IIR filter with two poles and two zeros; in practical terms, it’s a versatile filter that can have a wide variety of characteristics—lowpass, hipass, bandpass, notch, shelf, etc.—depending on the values of the coefficients in the filtering equation. But unless you’re a trained electrical engineer, you probably don’t know exactly how the coefficient values correspond to particular filtering characteristics.
If you want to change the coefficients of biquad~ in real time while a sound is playing, it's usually better to use MSP signals rather than individual Max messages, to avoid causing clicks. In that case, you should replace filtergraph~ with filtercoeff~ and send the frequency, gain, and Q parameters into filtercoeff~ as smooth signals (as shown in the left portion of the example).
This patch allows you to try out various filter settings of the biquad~ object, via the filtergraph~ object. For adjusting the parameters you can drag on filtergraph~ with the mouse, or you can send values in its three rightmost inlets for frequency, gain, and Q. The spectroscope~ object tries to draw the spectrum of the signal.