Small Capacitors in Guitar Amps

Your amp is filled with small capacitors as in the picture below.  They come in many different colours so this is jut a sample
In simple terms,  is in the filter circuits ( tone shaping) or to pass the audio ( AC) signal to the next stage of the amp while blocking the DC voltages. Values are typically in the range 0.001 to 0.47 uF.
In valve amps there are polyester, ceramic an silver mica capacitors.  Polyester came to the market in the 1960’s and other types have been around for decades longer.
The most common are silver mica capacitors.  These have to withstand the high voltages up to 450 volts and they have to block the DC voltage and let your music pass through.  In modern guitar amps, I have seen failure because the lead of the capacitor was bent to severely and I suspect moisture was absorbed over time and the capacitor went open circuit. Another simpler reason was that the bend in the lead resulted in the internal connection failing.
I have heard of folks finding that an old capacitor  values changed by 20% or more after squeezing it. ( these should be changed in the amp !) .  When this type of capacitor ages they can leak very small currents and what you hear in the amp is cracking an popping.  However, this can also be caused by noisy failing resistors, and electrolytic capacitors !  Tracking this type of fault down needs a signal generator and an oscilliscope and to go through each section of the amp in turn starting from the power supply then each stage starting at the input. If you don’t have this type of test equipment then find a good amp tech who has this gear and knows how to use it.