A cheap publication, comntaining melodramas written in a colourful and down-market style.
Penny dreadful is a rather dated expression and isn't a description that is aimed at publications these days, not least because you can no longer buy magazines for a penny.
The expression is American and came into use in the late 19th century as a pejorative term for the numerous cheap crime magazines that purveyed poorly written and hackneyed storylines. The establishment were critical of the time spent on such by the working classes, as this comment in the North American Review, 1861 indicates:
They can read the ‘penny dreadful’, but they cannot darn their stockings or mend their shoes.
The term has recently been co-opted as the title of a popular British-American drama television series.