ɑ=1-0.995=0.005, so ɑ/2=0.0025. This is the significance level. It corresponds to 1-0.0025=0.9975 confidence level (for a 2-tailed distribution) and from a normal distribution tables Z=2.81 gives us a probability of 0.9975. This means that 99.75% of the distribution (represented by the area under the distribution curve) is 2.81 standard deviations above or below the mean, giving a confidence interval of 2 times 0.9975=0.9950, that is, the width of the area below the distribution curve. We can be 99.5% confident that our data will be 2.81 standard deviations below or above the mean.
A 2-tailed distribution means that we are interested in the distribution on either side of the mean, and not just on one side or the other (only greater than or only less than).