What does a circuit's frequency response in dB refer to?
First lets honor the gentleman who gives the capital letter "B" to dB.  Alexander Graham Bell.

Sometimes it is useful to record power values in a logarithmic scale rather than a linear scale.  Example is 1 million to 1 ratio may be more useful to record in a logarithmic scale as 60dB instead of 1 000 000:1

Ratios of equivalent power units are expressed in dB.  So just like saying something is 1/100 you could say -20dB.  Or if something is 100/1 you could say +20dB.

Where some confusion arises is when the denominator is relative to some fixed value of power.  Example is RF power is usually relative to 1mW of power.  So 0dBm is 1mW, 10dBm is 10mW, 20 dBm is 100mW and 30 dBm is 1.0W of power.  Makes sense?  Honestly it is useful to engineers but very confusing to laymen.

Another source of confusion with the dB notation is when dealing with Voltage.  Remember I stated that ratios of equivalent power units are expressed in dB.  Power is proportional to the Voltage squared. So if you have a -20dB attenuator it is a 10:1 divider of voltage while it is also a 100:1 divider of power.  Again I'll say it is useful to engineers but very confusing to laymen.