For an average user this question is not only difficult to answer and explain but seldom useless. Consumer equipments are designed to have pleasing looks and they are meant to sound just pleasing. However these consumer equipment are seldom able to fulfill the needs of a serious music producer, audiophile and anyone who is seriously interested in the sound quality rather than looks.
It's not an easy task to understand the difference between the two based on just specs and features because at times these tend to give way more information than we require. So we will try to break down these important differences into simple pointers.
One of the most important reason for anyone to consider before buying a pro audio equipment is the Purpose. A Pro-Audio equipment is seldom meant to run in a home setting because its very rare to have 100 speakers running in parallel at your home. A home audio setting is supposed to switch from one input device to another very frequently. The connectors used are different as well. Amplifiers that are used for DJ's, touring concerts, etc. tend to have Neutrix Speakon connectors. Amps used for "installed sound" have screw-terminals or Phoenix terminal strips. Consumer amps tend to have screw terminals or some light-weight wire clip things. Consumer equipment uses (typically) unbalanced audio signals on RCA connectors while pro-audio tends to use balanced signals on XLR connectors.
The biggest problem with a consumer product is that very often the stated specifications rarely add up to the actual product, on the other hand, a pro-audio equipment is generally very high power and have exact specifications mentioned in the description. When rating the power of an amp there are a lot of ways that the specs can be fudged, and pro audio amps tend to fudge them less or if they are fudged then there is usually a footnote in the manual that explains exactly how the spec is measured.
This gets even worse when you consider car audio amps. The max power for a car amp is usually rated at 10% THD+Noise. Basically they crank up the power until the output is 10% THD+N and that is the spec that they quote. Home amps tend to spec the noise at 1% THD+N. Pro amps tend to go to 0.1% or 0.05% THD+N. Of course, there will be companies that do not follow these generalizations.
A Pro-Audio gear is built to last. They are intended to be used while touring, being bolted on various racks, able to handle extreme amount of mate-unmate cycles, and they are generally made of thicker housing material. These products are also meant to withstand more shocks, vibrations and extreme temperatures.
The electronics of a pro-audio gear is made likewise. They are built to last, able to survive decades of use. Consumer products...not so much. Pro-audio equipments are designed to be used in the most extreme settings. A pro-audio equipment is very unlikely to give up on you while you are touring or are about to step on stage in-front of a huge audience.
The reason why pro audio gear is a little costlier than consumer gear is because a pro-audio gear is supposed to have a lot more factor of safety than that in a consumer gear. What this means is that it can take up extreme conditions without failing.
Pro-gear is usually designed to handle a wide range of signal levels. Some mic signals are only 2 mV p-p, while other gear might be giving out 30 V p-p. This is a huge variation. Of course not all equipment is designed to take in the entire range of signals, but pro gear in general can handle the wider range much better than consumer gear.
A pro-gear can take up even in faintest signals from your instrument's transducer however a consumer gear will fail to do so. In certain situations this makes all the difference.
The most common nominal level for consumer audio equipment is −10 dBV, and the most common nominal level for professional equipment is +4 dBu (by convention, decibel values are written with an explicit sign symbol).
Expressed in absolute terms, a signal at −10 dBV is equivalent to a sine wave signal with a peak amplitude (VPK) of approximately 0.447 volts, or any general signal at 0.316 volts root mean square (VRMS). A signal at +4 dBu is equivalent to a sine wave signal with a peak amplitude of approximately 1.736 volts, or any general signal at approximately 1.228 VRMS.
Peak-to-peak (sometimes abbreviated as "p-p") amplitude (VPP) refers to the total voltage swing of a signal, which is double the peak amplitude of the signal. For instance, a signal with a peak amplitude of ±0.5 V has a p-p amplitude of 1.0 V.
Most equipment were designed to use a 600ohm impedance signals. Modern equipment, both consumer and pro, have low impedance outputs driving high-impedance inputs. For amplifiers, most consumer and pro gear can handle 4 and 8 ohm speaker impedance. Some pro audio gear can handle 2 ohm speaker as well.
The most important thing to be considered is +48V Phantom Power. Consumer gear is not designed to provide this at all, while it is pretty standard for pro gear to have one, that needs to connect to microphones. More importantly, most outputs on a pro-audio gear are designed to plug into inputs that can provide Phantom power, consumer gear cannot withstand that kind of power and is likely to be damaged if connected to a device with Phantom power.
As mentioned earlier, a consumer gear is designed to look and sound pleasing. Pleasing is a very broad term but for starters it means that it is designed to shun out all the frequency brackets that tend to sound annoying on prolonged listening. This means that the sound from the consumer product is more likely to give you an output that is good to hear but not necessarily accurate. A Pro Audio equipment is designed to serve only one purpose, to sound accurate. At times an accurate sounding system is not pleasant to hear and that's only because of the source signal. A consumer speaker system is highly likely to have a V curve in the generated spectrum and are often colored to be a little warm. Whereas Pro-Audio speakers are designed to give an honest and accurate sound with respect to the audio source and generally offer a very flat frequency response with little to no coloration to output signal.
To conclude, it's very important to first identify the kind of use you have for any kind of equipment that you are going to purchase and if you want to do some serious business, then a Pro-Audio system is worth spending the extra money for.
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