There has been a settlement at the site of where Cambridge is today since pre-Roman times.
Cambridge today is famous, and has been famous for centuries, for one thing: its university. The university itself has existed since around the 12th century, and its founding is in itself worth a mention.
Everyone knows about the term "Oxbridge" (the term dates from the 19th century, and was the tongue-in-cheek name of a university in a satirical novel), and the rivalry; but that rivalry infact was, most likely, born of booze. Oxford's university was founded by royal charter, and so attracted academics and students to the city. This was great for the town's intellectual reputation; it was also a boon for the boozers, too. After some time, the Oxford townspeople finally grew tired of the drunken antics of the students, and eventually some of the academics and students were forced out of the town. Banished from the intellectual Mecca of England, they chose Cambridge as their Medina; their place of exile and rebirth.
This was in the14th century. Oxford was the newer of the two cities, as it dated from Saxon times ("Ox-forde"); Cambridge, as I said, was ancient by comparison. Its original Roman name was Duroliponte; although there had been a settlement there before even then, and there are Bronze Age remains on the Gog and Magog hills just south of the city. After the Romans left, the Saxons built a town on the opposite side of the river ("Grantabrydge"), which eventually changed to Cambridge (Grantchester, a village just outside of Cambridge, still attests to this older name).
The "college" system developed over the centuries in Cambridge, as it did in Oxford. These days, Cambridge has 31 colleges; Oxford almost forty. Cambridge's oldest is Peterhouse; another half a dozen colleges were established over the middle ages, whereas much of the rest were established in the last two hundred years. Both universities act, effectively, as the custodians of their respective cities. The "college" system, for those unfamiliar with it, makes the University seem similar in arrangement to a semi-autonomous, federal republic - all the colleges are autonomous of their own budget and have their own rules and specialisations, but all fall under the umbrella of the University (arriving students are either advised which college to choose, or a suitable one is chosen for them).
A few random facts and observations about Cambridge:
1) Cambridge is the driest place in the UK; it has the smallest amount of rainfall, which maybe also explains why cycling is so common here - you're more likely to cycle if you're more certain you won't get wet.
2) Cambridge University is, apparently, the largest landowner in the UK after the Church Of England. Much of the housing development that goes on in the city is due to the University's guidance. The same goes for the "Silicon Fen"; the UK's largest IT park, also linked to the University; as well as the Science Park.
3) Cambridge is a city of around 100,000 people; Oxford slightly more. Cambridge is about pubs, churches, colleges, parks, punting and cafes. It sounds as English as you can get, but the atmosphere is extremely cosmopolitan, with a huge foreign population; students, workers, whatever. That makes the city feel very liberal; maybe surprising for a place that seems at first to represent everything about the "old establishment". It's also a Liberal city - the council has been solidly LibDem (with a Labour minority) for twenty years, with not a Tory in sight (though to be fair, Oxford has been run by a Labour council for a similar period).
4) The atmosphere in the city is therefore unique; like Oxford, though for slightly different reasons. Cambridge feels like a country town, but still has a sizeable city centre. The river dominates the city, as it runs right through the town centre, and gives plenty of space for open parkland.
While Oxford and Cambridge share many similarities, they differ on a few points.
First, the setting is different: Cambridge lies in lowland, close to the fens - as a result, the landscape looks almost like from a Dutch or Flemish painting; Oxford, meanwhile lies in a valley of low hills - a kind comparison might be to the south of France or Tuscany.
Second, the architecture of the cities are different: Oxford's style is fairly uniform - in a medieval renaissance civic style, with a city centre of graceful streets, squares and parks. By comparison, Cambridge is more like a medieval country town, with the colleges in a more varied and eclectic style, like ducal courts and palace complexes designed by a plethora of competing architects.
Lastly, both cities had important but opposing roles in forming the nation's political history. During the Civil War, Oxford became the seat of King Charles' court - in effect, the official capital during his war with Parliament (though, to be fair, many people in Oxford did not approve of the king either); meanwhile, as Cambridge was the centre of Cromwell's Eastern Association (Cromwell came from nearby Huntingdon), it acted as the unofficial "capital" of the Republican cause. Although it is a simplification to say so, symbolically, Oxford was the king's city; Cambridge was the ideological capital of the Parliament, and the English Republic.
In other words, Cambridge is the spiritual home of English republicanism.