350 words.

In the discourse on Enterprise Risk Management, definitions of risk tolerance can border on the absurd, showing a slavish adoption of financial terminology where it makes no sense.

Risk tolerance in finance
The degree of risk tolerance, whether at the individual or organizational level, describes whether you are relatively:
1) risk-averse (risk avoiding) in exchange for a degree of certainty regarding the reward in question; or
2) risk-seeking, (accepting of risk) in exchange for the chance of higher gains.

These orientations towards uncertainty can be expressed quantitatively and categorized qualitatively. For example, financial advisors attempt to gauge an individual’s “investor profile” (tolerance for risk) in two aspects:
a) mental attitude towards risk (converted to a level) using a questionnaire; and
b) financial position, using a calculator.

Similarly, investment fund managers:
a) describe the strategy of a fund as relatively aggressive (risk-seeking) or conservative (risk-averse); and
b) have internal limits (risk appetite) dictating how much capital they will risk.

Therefore, risk tolerance might be articulated by: 1. a general characterization of attitude or philosophy; and 2. corresponding measures of degrees of resource allocation and investment.

Levels of investment against anticipated return are controllable. Here, corporate statements of risk tolerance and appetite as specific numbers make sense. 

Risk tolerance applied generally
I believe that the notion of risk tolerance is translated into non-financial domains literally and often inappropriately. Because of the rhetoric, health care and other public sector agencies feel pressured to define a positive number indicating, absurdly,  “tolerance” for children at risk, wait-listed patients, or traffic deaths. Some want to assign a dollar value to human life. Then again, declaring “zero tolerance” implies a strict attitude to abhor and punish one or another social ill, but, of course, cannot confer unlimited capacity to prevent it.

Risk tolerance was imported from finance to ERM, and so may not be strictly appropriate in all contexts. 

Practical advice
Where sensible, it is possible during the risk assessment to state tolerance for each line item simply as high, medium or low, using the organization's criteria (i.e., goals, values, ethical code, etc.). It is one of four tests that determine the response to the risk.

Notes
Please see related post: Risk Tolerance: Non-Finance Examples