The tails are named for the two sides of a parabola that extend far from the central hump of the curve. The lines are continuous and have the potential to extend for infinity based on the shape of the curve. The tails can begin at different levels of the curve according to different levels of scientific rigor. However, most experiments require at least two standard deviations, which would be equivalent to 5 percent and 95 percent levels of the curve.
The null hypothesis is the default position of an experiment with a two-tailed hypothesis. A new theory involves the rejection of the null hypothesis. For example, a null hypothesis might be that gravity accelerates objects at a rate of 9.8 m per second squared. To reject the null hypothesis, many experiments would be taken. If there were significantly more readings above and below the number suggested by the two tailed hypothesis, than the null hypothesis could be rejected and a new speed could be provided.
A two-tailed hypothesis can be a standard "Gaussian" curve or a more chaotic curve with an entire data set. When the Gaussian curve is used, a T test is used to determine if the null hypothesis is rejected. When the entire data set is used, a Z test is used to determine whether the null hypothesis is rejected. Each test has an associated statistical table that correlates to the standard deviation of the data.
A one-tailed test is also a powerful tool for evaluating hypotheses. However, these are used when you are only testing the data in one direction. This can be useful and meaningful in many instances. For example, if you are testing a new drug you may only want to test that it is not less effective than the current market alternative. In other words, for approval you do not need to test if the drug is significantly better than the alternative, only if it is worse.