
Jupiter (or Jove) was the top baboon amongst the Gods (Greek name: Zeus). He spent his time carousing, drinking, zapping people with lightning bolts, and changing himself into various animals so he could have sex with nymphs, goddesses, and hapless human women. He was the quintessential party animal. He was the Roman god of justice, law, and social order, which says a lot about Roman ideas of social order; nymph, anyone? 'Jovial' is still commonly used to describe someone who is jolly or optimistic. Naturally, Jupiter in a natal chart will describe where, and how, the individual has a 'do it BIG' mentality. Whether in the natal chart or in a transit to the chart, Jupiter expands whatever it touches, be that emotions, or money, or your waistline.
Saturn, on the other hand, was Jupiter's father. He tried to eat Jupiter when Jupiter was an infant, but his tricky wife gave Saturn a lump of rock wrapped in swaddling instead. Saturn, apparently, couldn't taste the difference. Eventually, Jupiter bested Saturn to become King of the Gods. Saturn has been grumpy ever since, probably because he's wondering what that lump is, rolling around in his intestines.
Originally, Saturn was the god of agriculture, but in astrological terms Saturn has a very different role: that of the Greater Malefic, the Limiter, the Bringer of Obstacles and Hard Times. He is a tough taskmaster. Whereas Jupiter's natural tendency is to 'overdo' whatever it is that Jupiter is doing (generally in an optimistic spirit of, "Whoo-hoo! Yeah! Let's do it!"), Saturn is the opposite: he brings us down to earth with a bang, he makes us wipe our collective noses and stand up straight ("Booo!")
Jupiter/Saturn aspects in a natal chart can tell us something of the conflicting energies of these two planets, and whether the conflict between optimism and pessimism can be worked out harmoniously or not.
In my natal chart, Jupiter is opposing Saturn. Whilst this might be seen to be an elegant description of the original mythology at play, the ramifications can be a little less elegant. Whenever an individual has Jupiter opposite Saturn in the natal chart, the inherent 'push/pull' conflict continues forever and ever. Because an opposition is considered an unstable aspect (balancing the two opposites), the individual tends to swing back and forth between the two sides, or at best finds an uneasy middle ground that can be knocked off-balance again very quickly. Often, people end up 'doing' one side more often than the other, and this becomes an habitual modus operandi.
The houses where you find Jupiter and Saturn in opposition will tell you 'where' in the arena of life this yo-yo-ing will take place. I have gloomy Saturn in my 3rd house: my 'thinking' box. Saturn is conjunct my Moon, so I have a double-whammy of feeling/thinking (emotional Moon in a cerebral house) and having the Gloom-meister in the same box. So you could say, in a nutshell, that my feelings and thoughts are repressed; or rather, that I keep a tight grip around my own subjective perspective. I am emotionally guarded; I keep my deepest thoughts to myself, and tend to not trust my feelings. Saturn in the 3rd tends to make people worry about being stupid, so they try very hard to either get smart, or at least appear smart.
Jupiter, on the other hand, sits in its 'natural' house, the 9th: Jupiter's house. Jupiter feels right at home there, the house of long distance journeys of the body and mind, the house of philosophy and law. I like this Jupiter placement. Jupiter in the 9th gives people a strong religious bent (or an interest in religion and spirituality): Beatle George Harrison had Jupiter here. We like studying. We like travelling. We like tripping the light fantastic. We like to do it often.
So what do you get when philosophy is in eternal conflict with garden-variety thinking? To put it simply: A Troubled Mind.
There is some evidence to show that Jupiter/Saturn oppositions can result in manic depression, now called Bipolar Disorder; but it isn't a guarantee of being or becoming bipolar. I had what I would term a 'manic episode' during a very long depressive phase, wherein I maxed out my student loans and spent the funds on shoes and clothes and beauty products. I don't have any of the shoes anymore (and one could argue that the beauty products didn't do what they said on the tin), but I still have the loans to prove I did, once upon a time, have a fine collection of shoes. Am I a manic depressive? Nope. But because I have my natal Moon so close to Saturn, this expand/repress action was manifested through an inappropriate expression of thinking/feeling. Shopping was a (costly) Band-aid.
The individual with this aspect will tend to swing from optimism to pessimism, and back again. They will dream Big Dreams and then Saturn will poke a pin into the bubble and ask to see the business plan. This can cause no end of disappointment and can sometimes lead to a chronic lack of faith in oneself; the optimism can never seem to get the upper hand on the pessimism.
My maternal grandmother also had this aspect. She was a Sagittarius like me, and coincidentally or not, had a Saturn/Jupiter opposition in the same signs that I do (Saturn in Taurus and Jupiter in Scorpio). She never knew her time of birth, so we'll never know for sure which houses Jupiter and Saturn were in, in her chart. But this doesn't stop us from seeing how it worked in her chart.

I always knew Gran to be supremely practical: from the Depression generation, she knew how to save a dollar, and to stretch one. One of her biggest disappointments, she told me, was that she was never able to travel as much as she had wanted to: that old Saturn made sure she stayed 'responsible', taking care of business and everyone else, so she lived her dreams of foreign travel through me, her ever-wandering grandchild. She even bought my tickets for me. There were times when I was sure that she wasn't allowing herself to have fun; she would turn down outings or going out to eat. Since when does a Sagittarius turn down either travel or food?
One of the last things she told me before she died was, "I guess I didn't have much fun in life," which besides being incredibly sad, is a testament to how difficult it can be to find the balance between Jupiter and Saturn. She never understood my depressions; in hindsight, I think it's fair to say that she was depressed a lot of the time, but never knew what to call it.
When Gran died, I took some of her ashes with me back to England, and cast them into the wind along the side of the M11, in a field on a hill. Gran didn't get to travel enough in life; but in death she got to travel at last. Her Jupiter would have been pleased.