The result of a hypothesis test is “significant” if it would be unlikely to observe a result at least that extreme if there were no actual effect to observe. A significant result tells you that the effect probably does exist, but that's all - notably, it tells you nothing about the effect size.
The “significance level” (denoted α) of a study is the probability of that study rejecting the null hypothesis H₀ given that H₀ is true (low is good).
The “p-value” of a given result is the probability of obtaining a result that extreme given that H₀ is true (low is good).