Royes,
When you establish your alpha risk level (i.e. p = 0.05) what you are saying in paractical terms is that you do not want to reject the null hypothesis until you are 95% sure it is safe to do so. Or the inverse, you are only willing to take up to a 5% chance that rejecting the null is the wrong thing to do. So if the p-value is less than .05 (less than 5% chance) then you can safely reject the null and accept the alternate hypothesis based on the data you have collected.
That is somewhat of an over simplified explanation, but hopefully that helps.
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