Suppose the random variable has the standard normal distribution, . Pick any real number, say . What is the probability of the event ? The answer is , i.e. , as any high school student will tell you. So the event has probability , that is almost surely.
Do you think this means that it is impossible for to be exactly ? You may say yes, and you may be right, but then the same is true for any other value. You are left wondering how it is possible for to take any value whatsoever, given that it's impossible for to take any particular value.
Do you begin to see the difference between the terms surely and almost surely?