It would make sense to use a semicolon to separate independent clauses that already contains commas or between items in a series that already contain commas.
We, your unsung heroes, wouldn't imply that it's time for you to hop on the bandwagon, face the music, and sing a different tune; but we are not whistling Dixie when we say it's time for you, Johnny One-Note, to know your brass from your oboe.
Although we have tried to explain in a tasteful, melodious manner the distinctions among introducing marks of punctuation, such as commas, colons, and dashes; separating marks, such as commas, semicolons, and periods; and end-of-sentence marks, such as periods, question marks, you probably still feel that this book is filled with too much sax and violins.
In the sentence you quote, though, "a lion, an eagle, a badger, and a snake surrounding a large letter H" describes the coat of arms, and the semicolon is wrong. In that case a comma should be used. Somebody would also prefer using a colon.
The past night I dreamed a hippogriff, the legendary creature which resembles a winged horse with the head and upper body of an eagle.
The past night I dreamed a hippogriff: the legendary creature which resembles a winged horse with the head and upper body of an eagle.
The examples have been taken from "Comma Sense, A fun-damental guide to punctuation."