If you choose to minimise a risk, you accept that it can't be eliminated, but take action to reduce its probability or negative impact (or both). Minimising probability means taking actions so that a negative outcome is less likely to occur; minimising impact means taking actions so that the consequences will be less severe if a negative outcome does occur.
We can see this in action by considering our own lifestyle choices. By choosing a healthy diet and exercising well, we minimise the probability of health problems in later life. By taking out health insurance, we hope to minimise the impact if they do occur. Clearly, we could do both these things - minimising both probability and impact as a result. How much action we take to minimise a risk, and the kind of actions we favour, depends on our own priorities, plus (as always) our assessment of probability and impact. If our past medical history suggested we were more at risk from health problems, we might be more motivated to take action.
A parallel from business would be typical responses to operational risks. Employees should be protected from physical harm wherever possible (minimising probability), but the employer is also obliged to have systems in place to deal with injuries should they occur (minimising impact).
Another example of minimising impact is double redundancy in computer systems. Here an entire duplicate system is created and maintained, so that it can take over in the event of malfunction. This hugely reduces the potential impact (though not the probability) of crucial data systems going offline; there is of course a trade-off in terms of cost. This is often the case: in general, the more you reduce impact, the more cost is involved. The business might choose to instate a repair contract with an IT service company instead, but this would not provide the same reduction of impact as the double-redundancy system.
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