From my understanding (I might be very wrong), the "earth" in alkaline earth metals means non-metallic, insoluble in water, and resistant to heating, therefore the oxides and hydroxides of group 2 metals should be insoluble in water by definition of "earth".
However, doesn't the term "alkaline" by definition mean bases that are soluble in water? How can the two definitions be co-applicable?
"Insoluble (in water)" is a relative term, especially for ionic compounds, and so is "alkaline". That relativeness gives us enough wiggle room for two of our most common bases to slip through.
Roughly speaking, it takes a thousand volumes of water to react with and then dissolve one volume of calcium oxide, so the solubility of lime in water would not be evident from casual observation. Yet if you put an indicator into the water it reacts in a way that indicates the water has turned alkaline. The solubility of lime in water is hard to see with the eye, but it overwhelms the tiny intrinsic autoionization of water, so lime gives evidence of being both an "earth" and "alkaline". Ditto (despite the still lower solubility) for magnesia.
Lime and magnesia, then, are the quintessential alkaline earths, far exceeding anything else with similar properties in their common occurrence. They have become the namesake of all the "alkaline earth metals" in Group 2.
This definition has a historical origin, as these names have been given in the $18$th and $19$th century. In the $18$th and $19$th century, oxides and hydroxides were not always separated. Hydroxides were often considered as hydrated oxides, like salts were known sometimes as anhydrous and sometimes hydrated. Metallic oxides and hydroxides were not considered really different.
In these old times, the oxides (or hydroxides) were known and studied before the elements were discovered. So first alkaline oxides (or hydroxides) were found to be very soluble and strongly alkaline. Then earths were similar to alumina (aluminum oxide) which is insoluble in water and neither basic nor acidic. But aluminum oxide (or hydroxide) neutralizes acids somewhat like an alkaline hydroxide. So there is a common character to alkaline hydroxides and earths : the reaction with acids, making salts.
Well, now, chalk, magnesia and baryta (oxides or hydroxides) are half way between alkaline hydroxides and earths : they are a little soluble, and this behavior is between soluble alkaline hydroxide and insoluble earths. Furthermore, chalk, magnesia and baryta react with acids like alkaline hydroxide and earths. So these oxides and hydroxides are intermediate between alkaline compounds and earths. This is why they are called "alkaline earths". Later on, the same name have been given to the metal, when the corresponding metal has been produced, usually by electrolysis.
An alkaline substance doesn't always have to dissolve in water(or at least very well), for example, copper(II) hydroxide, as shown in Wikipedia is negligible.
But then there are bases like sodium hydroxide and potassium hydroxide which are quite soluble.
Wikipedia says:
An alkali can also be defined as a base that dissolves in water. Alkalis are normally water-soluble, although some like barium carbonate are only soluble when reacting with an acidic aqueous solution.
More information below:
