In statistics, a result is called significant if it is unlikely to have occurred by chance.  "A<unk> ly significant difference" simply means there is<unk>  evidence that there is a difference;  it does not mean the difference is necessarily large, important or significant in the usual sense of the word.
In traditional frequentist<unk>  hypothesis testing, the<unk>  level of a test is the maximum probability, assuming the null hypothesis, that the statistic would be observed. Hence, the<unk>  level is the probability that the null hypothesis will be rejected in error when it is true (a decision known as a Type I error, or "false positive").  The<unk>  of a result is also called its p-value; the smaller the p-value, the more significant the result is said to be.<unk>  is usually represented by the Greek symbol, α (alpha).  Popular levels of<unk>  are 5%, 1% and 0.1%. If a test of<unk>  gives a p-value lower than the α-level, the null hypothesis is rejected. Such results are informally referred to as<unk> ly significant'.  For example, if someone argues that "there's only one chance in a thousand this could have happened by coincidence," a 0.1% level of<unk>  is being implied.  The lower the<unk>  level, the stronger the evidence.
Different α-levels have different advantages and disadvantages. A very small α-level (say 1%) is less likely to be more extreme than the critical value and so is more significant than high α-level values (say 5%). However, smaller α-levels run greater risks of failing to reject a false null hypothesis (a Type II error, or "false negative"), and so have less<unk>  power. The selection of an α-level inevitably involves a compromise between<unk>  and power, and consequently between the Type I error and the Type II error.
Statistical significance
Number needed to treat
Median
P-value
Absolute deviation
Sensitivity 
Average
Absolute risk reduction