Systematic Risk (aka Undiversifiable Risk)
Systematic risk is a risk that cannot be diversified away - this is why it's often called diversifiable risk. That's a nice definition, but what does it really mean? Let's dig deep to understand this crucial term.
Systematic risk is a vulnerability to things that can occur at a macro or aggregate level - things that affect not only the size of a specific slice of the pie but the overall size of the entire pie. Systematic risks arise because the world is stochastic (random) in nature and as we move forward in time, things can possibly occur that will not only have micro effects (eg. affecting a city, a specific firm, a specific industry, etc.) but will affect the entire economy as a whole (eg. the entire nation or the entire globe). Stated another way, systematic risk is the risk that the overall size of the economic pie will be affected - instead of only affecting the distribution of it.
What can affect the size of the matter? That's easy to answer. Things that can affect the pie are generally events that have macro impacts:
All of these things would invariably affect everything - the overall economy would be affected. Yes, individual firms, businesses, cities, states, and counties would be affected, but they would only be affected because the entire global economy is affected and not because of their own foolishness or bad luck. Therefore, we can say that systematic risk is the kind of risk you can't really hide from - this is why it's called diversifiable risk.
Imagine a person or a firm tries to diversify away risks and protect themselves from all of the possible negative things that could occur. Say they make sure spread their money into different places, get income from different sources, be prudent about capital purchases and how they are financed, and investing in a vast variety of things (things such as precious metals, stocks, bonds, real estate, private equity, etc.). all to these things would clearly protect whoever is doing them - a drop in gold wouldn't affect them, nor would the drying up of a certain source of income, and nor would the bankruptcy of an individual firm. The person or firm engaging in the above actions would be so diversified that they would hardly feel the effects of a small catastrophe. However, they are still totally exposed to the risks we described above - a major war, a comment, an alien invasion, or deep geopolitical troubles would impact them regardless because everything they own would lose value. They would be affected not because of the loss of a single slice, but because the entire pie would now be smaller than before.
Imagine a probability distribution - the x-axis represents wealth and the y-axis represents the number of people who have that amount of wealth. The area under the curve would be the total wealth in the society in effect. You're unsure of where you'll end up - maybe in the middle but you hope to end up on the far right. Systematic risk is the risk that you'll be affected no matter where you are - it's the risk that the entire distribution will get smaller (that the overall area under the curve will be smaller).
Unsystematic Risk (aka Diversifiable Risk)
Unlike systematic risk, unsystematic risk is a specific type of risk that is present only at a micro level. This type of risk can be that:
All of the above risks are obviously severe (and will obviously be unpleasant to those experiencing their realization), but they only affect a small number of firms and a small number of people. A person who owns no gold, hasn't invested in that stock, or didn't buy that bond won't care about any of the above risks - they'll be totally fine no matter any of the above potential scenarios. The risks, therefore, are not systematic in nature but are rightly called unsystematic or specific risks.
These risks are also called diversifiable risks. We stated above that you can't diversify away systematic risks - no matter what you do you're exposed to those large-scale risks that could make the entire pie smaller (that would affect the overall amount of resources instead fo just affecting the place in the distribution). You can, however, diversify away unsystematic risk - you diversify in investing, for example, by:
You will always be exposed to systematic risks, but you don't have to be exposed to unsystematic risk at all - you can simply diversify it away. By not diversifying, however, you are exposed to both systematic and unsystematic risk - not only are you exposed to the macro systematic risks, but you're also exposed to the risk of the particular investment you're holding.