Two comments:

(1) Every distribution can be locally represented as a (distributional) partial derivative of a continuous function. For example, for the dirac delta at 0, we can start from the function which is 0 for negative x, and equal to x for positive x and take two derivatives. Therefore, it is important to understand that not all distributions are made equal -- the more complicated ones are made by taking more derivatives of continuous functions.

(2) Some examples to definitely keep in mind (to emphasize the subtleness of the notion) while thinking about distributions are the principal value p.v $\frac{1}{x}$ and the pseudofunctions p.f. $\frac{1}{x^n}$