Something that is periodic (1) happens at regular intervals, or (2) is intermittent. Periodical means published at regular intervals, and it doubles as a noun referring to something that is published at regular intervals. The words were originally variants of each other, and some dictionaries still list periodical as a variant of periodic, but they are generally kept separate in 21st-century usage.
Periodic and periodical constitute just one of many -ic and -ical word pairs that are frustratingly inconsistent. Economic–economical and historic–historical, for example, have undergone differentiation similar to that if periodical and periodic. Meanwhile, ironical is an unnecessary variant of ironic, and metaphoric is an unnecessary variant of metaphorical. There are no rules to explain these developments. Each word pair has had its own trajectory.
The standing ovation lasted for nearly 20 minutes, punctuated by periodic shouts of “bravo” from ecstatic members of a most satisfied crowd. [Scotsman]
The periodical also posted scanned pages bearing the signatures of the gathered tribal elder. [Wall Street Journal]
Our government is accountable to the people through periodic elections, and is continually accountable to our representatives in Parliament. [Ottawa Citizen]
According to the Oxford English Dictionary, it was Marxist periodicals of the 1920s that adopted “exceptionalism.” [Salon]
It also didn’t help that she suffered from periodic anxiety attacks. [New Zealand Herald]