When you do something periodically, you do it either occasionally or at regular intervals. Do you talk to your grandmother once every week or two? Then you can say you call her periodically.
It's easy to get to the bottom of periodically by looking at the word period, in its sense of "course or extent of time." When things happen periodically, they occur after a period of time has passed, either a random length of time or a more regular interval: "That bird shows up at my window periodically" or "He periodically opens and closes the blinds just as the sun rises and sets."