An alpha or significance level of 0.05 corresponds to a 95% confidence level. 0.01 corresponds to a 99% confidence level. If a vaccine is said to offer 80% immunity to a particular life-threatening disease then at a 95% confidence level, you would be confident in 19 out of 20 samples of vaccinated people that 4 in 5 people in the sample would become immune to the disease. But at a 99% confidence level you would be more confident, that is, in 99 out of 100 samples of vaccinated people that 4 in 5 people would become immune. It's clearly better in what could be a life or death situation to have a higher confidence level (a lower alpha level).
By contrast, consider a weather forecast. A 95% confidence level about the 60% possibility of rain on a particular day isn't usually a life or death situation, although it might have some significance for farmers or mountain climbers, for example, so the degree of confidence may not need to be particularly high. A hurricane or typhoon forecast, however, may need to have a higher confidence level for the safety of a community or shipping, for example, so a 99% confidence level may be preferable (if that's possible).