Speculative risk is a key feature of the vast majority of investments. It simply refers to the risk that an investment may lead to a profit or a loss. This differs from "pure risk," which refers to events that are guaranteed to cause some form of loss. With pure risk, the risk is whether or not the event happens.
The easiest way to tell the difference between the two types of risk is the types of outcome that are possible, and whether the risk is voluntary. Pure risk only leads to negative outcomes and is an inevitable part of life. Speculative risk has the potential to create positive or negative outcomes and is entered into on a voluntary basis.
Theoretically, pure and speculative risk can exist in any form and any walk of life. In most contexts, however, they are assessed in financial terms. Asking somebody on a date is a speculative risk that could pay off by leading to a relationship or result in a negative result of being rejected. This wouldn't usually be assessed in financial terms, however, so does not fall under most analysis of the two types of risk.
Within finance, pure risk is usually associated with insurance. This deals with the outcome of unpredictable events that have a negative outcome, such as injury, theft or fire. Insurers calculate premiums by combining the likelihood of the event happening with the financial loss that would result.
Speculative risk is usually associated with investment, which nearly always carries the possibility of making a profit or loss. The degree of risk can vary immensely. Spread betting, a form of gambling on market movements, can be very risky as the profits or losses can vastly outweigh money staked. Buying a government-issued bond is much less risky, though there is still a tiny risk that the government might not repay the cash, however unlikely that is.
The two types of risk have arguably been blurred together by the increasing integration of the insurance and investment markets. For example, many insurers are now publicly traded companies. This means that stockholders are taking a speculative risk that ultimately derives from the performance of the company. This performance, however, is strongly linked to the pure risk borne by insurers, which is that the covered events will indeed happen, causing it to make payouts. The convergence of the two types of risk has increased due to the introduction of products such as catastrophe derivatives, which are effectively a form of gambling on the losses suffered by insurers.