First the easy bit - exaltation is one of the essential dignities, like sign rulership. Indeed Lee Lehman in her book, Essential Dignities, says that there is evidence for exaltation being at least as old, if not older, than the dignity of sign rulership. Modern Astrologers do seem to recognise it but they tend not to really use it in any systematic way.
How the system of exaltation evolved is difficult to say, and indeed it's arguable whether there's any system to it. Ptolemy wrote that the Sun was in exaltation in Aries because when it entered that sign it moved from the Southern hemisphere into the Northern hemisphere - Spring andSummer were coming (don't forget that Western Astrology developed in the Northern hemisphere).
With the Sun having exaltation in Aries, it's opposite planet, Saturn, (then believed to mark the limit of the solar system) was given exaltation in Libra, the opposite sign (and the sign in which the Sun recrosses into the Southern hemisphere, bringing Autumn and Winter to the North).
The Moon has exaltation in Taurus. According to Ptolemy, the reasoning is as follows, imagine the Moon in Conjunction with the Sun in Aries - a New Moon, so the Moon can't be seen - it's first phase of visibility is when it enters Taurus. Now as the Moon moves from the conjunction with the Sun it grows in visibility - so here we have a Moon which is becoming bigger each day from now on and more potent. Moreover Taurus is an Earth sign and the Moon rules the Earth Triplicity by night (another form of dignity).
However, thereafter the reasoning becomes vague - Apparantly Jupiter is in exaltation in Cancer because this is it's furthest North declination - but Jupiter's exaltation squares that of the Sun, which seems odd when their sign rulerships are in trine.
Mars is given exaltation in Capricorn because this is it's furthest South declination - possibly because as a malefic planet it is going to do less damage in a cold and dry place the other side of the equator.
Venus has exaltation in Pisces, for no clear reason I have identified and Mercury has exaltation in Virgo (which it also rules).
To make matters more murky some writers, such as the Arab Astrologer, Al-Biruni attribute specific degrees to exaltations but don't seem to provide an explanation. Whether this is because at the time it was so obvious that it didn't need explaining or whether it was because the reasons had already been lost is not clear.
I do use the exaltations but I also recognise that there's not the clear explanation that exists for sign rulership. Oddly modern Astrologers seem to have done little with exaltations that have little system, whilst changing the traditional system of sign rulerships which has clear and logical reasons and replacing it with something that is as unsystematic as the exaltations.
PS this was not a 'stupid' question - it was a very good one, there are Astrologers out there who try to use the exaltations without any knowledge of why they are there or whether there is an underlying system.