According to EtymOnline, the phrase continental breakfast is from 1911:
1818 as a purely geographical term, from continent + -al (1). In reference to the European mainland (as opposed to Great Britain), recorded from 1760. Continental breakfast (the kind eaten on the continent as opposed to the kind eaten in Britain) is from 1911.
I do doubt whether this estimate of the term's origin is correct. There are instances of it in The Sanitarian", which was written in 1896:
There is also an instance of it in the Philadelphia Friends' Intelligencer in 1877:
It is possible that the term is even older, though probably not by much. In any case, the continent refers to the European mainland. So a continental breakfast is the breakfast eaten on this continent. According to Wikipedia, this meal is:
a meal based on lighter Mediterranean breakfast traditions. It is a light meal meant to satisfy one until lunch. A typical continental breakfast consists of coffee and milk (often mixed as cappuccino or latte) or hot chocolate with a variety of sweet cakes such as waffles/pancakes, brioche and starchy foods such as croissants, often with a sweet jam, cream, or chocolate filling. It is often served with juice. The continental breakfast may also include sliced cold meats, such as salami or ham, yogurt or cereal, or a slice of cheese. Some countries of Europe, such as the Netherlands and those in Scandinavia, add fruit and cheese to the bread menu and occasionally a boiled egg or a small serving of salami.
It is unclear whether this is the original contents of such a meal. However, it seems that an English breakfast is different:
Traditionally, people in the United Kingdom and Ireland have enjoyed a substantial hot meal for breakfast, featuring eggs, bacon, and sausages, accompanied by toast and tea or coffee. These items are sometimes eaten separately on morning rolls. In Britain, this was traditionally known as an English breakfast
Frommer's Bed and Breakfast in the Mid-Atlantic: A Selective, Full-Color Guide to the Best of New York, New Jersey, Pennsylvania, Washington, D.C., Maryland, and Virginia
Book (Macmillian Travel Books)
DualSpices English Breakfast Black Tea 3.2 Oz (40 Cups,19 Cents/Cup) Loose Leaf Tea.
Cuisinart DCC-2800 Perfec Temp 14-Cup Programmable Coffeemaker, Black