Full of Beans: Lively, energetic, in high spirits, as in "The children were full of beans today, looking forward to their field trip". This expression has no valid explanation. (circa 1840). -- From www.answers.com
Well, that about sums it up. This expression does indeed have no valid explanation. However, humans are not so worried about 'valid', so we do have a not-so-valid explanation that has run rampant across the internets.
Maybe it has something to do with horses! Since time immemorial, people have known that if you mix beans into a horse's feed it will grow stronger and have more energy. the beans have a high protein content, which helps the horse build muscle and repair tissue damaged during heavy exercise. Thus, the term could have been used to refer to those strong horses that were quite literally full of beans. Of course, we have no evidence that this is the true origin. It is worth noting that horses are also often associated, probably falsely, with the expression 'feeling one's oats', which most likely comes to us as a corruption of 'to sow your wild oats'. 'Feeling one's oats' is largely synonymous with 'full of beans', and it is sometimes assumed to have come from the fact that horses are more lively after feeding... Sound familiar?
The horse theory could be correct, but it is easy to make up etymologies. To demonstrate this, I went ahead and made up another origin myth -- who knows, it may even be true. Just to be clear, every part of this alternative explanation is true, we just don't have any evidence that it is related to the expression.
Maybe it has to do with Twelfth Night! For centuries it was an European tradition for employers to give a feast for their employees on the Twelfth Night. In England this was known as a bean-feast, after the bean hidden in the Twelfth-Night cake. The people who found the beans (always one male and one female; two cakes were baked so that there would be no odd pairings) were the king and queen of the feast, known as the 'The King of the Bean' and 'The Queen of the Bean'. These lucky winners played the role of the lord of the manor for the night, dressing in their masters' clothes and giving mock orders. Eventually, 'bean-feast' came to mean any celebration or festive occasion, and the traditional bean was replaced by a small coin baked into in holiday cakes and puddings. Bean feasts are also the origin of the UK expression 'beano'. It would be a small jump to imagine that the king and queen of the feast might be said to be 'feeling full of beans', and that this phrase could easily cross the Atlantic...
Full of Beans: Stupid; Erroneous; Misinformed.
"Feeling one's beans" is also sometimes used to mean that someone is acting foolish, talking nonsense, or being stupid. This appears to be a newer usage, but it has become quite common. This sense of the phrase may be familiar to most of us from A Christmas Story ("You're full of beans, and so's your old man!"), but it has been used on both sides of the Atlantic for decades.
Unsurprisingly, we don't know the origin of this usage either. It may simply be a mis-application of the older sense of the phrase, or it may be a humorous variation on 'full of hot air' ('cus beans give you gas, you see). In any case, be careful when telling someone that they are full of beans, they may not think it means what you think it means.