A sportive is a cycling event over a medium to long distance that is open to the general public. It is not a race but the events will often be timed and officially signed. The biggest and most organised sportives will take place on closed roads so that riders do not have to worry about other traffic.
There is no single defined standard for a sportive. A sportive may have as few as 50 riders who are handed maps at the start and ride in groups around the course. The most famous sportives - for example the Etape du Tour and La Marmotte - will have nearly 10,000 cyclists taking part and will have a start village, police escorts, medical support, prizes and award ceremonies for the fastest finishers.
Sportives will generally be from about 50 miles at their shortest to as far as 200 miles in a day. Sportives can take place over multiple days - for example the London to Paris ride or the Lands End to John O'Groats ride.
Generally speaking, sportive organisers will put up signs around the course to show riders where to go and organise food stations so that riders can stock up with water and high energy foods, rather than have to carry around their own supplies or stop at shops and cafes on the way round the course.
There is normally a fee to enter a sportive. This can be as low as £8 and as high as £150, depending on who is organising it and what they supply. Many sportives are organised to raise money for charity although some are purely commercial ventures. The more you pay, the more you can expect to have a professionally run event with photographers, changing rooms and showers, bike washing equipment, technical support, well stocked food stations and so on - but it isn't guaranteed and it is worth checking reviews of previous events to see what an event's reputation is before parting with your entry money.
For many people sportives are their first route into the world of semi-organised cycling. The vast majority of riders are initially setting themselves the target of finishing a long ride. Club riders often use sportives to test their fitness against other club riders and to ride in bigger groups and with different people to their normal weekly ride. While there are always some people who will aim to finish a sportive as quickly as possible - sometimes with not much regard for their own safety in doing so - I would say that almost everyone else is doing it for their own satisfaction and are not taking them incredibly seriously. My experience of sportives is that they are great fun (even when it is pouring with rain and you are riding into a 30mph headwind) and you get to ride with and chat to a wide range of people who share your interest in cycling.
The name sportive is a shortening of cyclosportive, the French term for the same event. In fact in French the full name is randonnée cyclosportive. You will also find the events called cyclosportif in Continental Europe. In north America sportives are better known as Gran Fondos, the Italian name for "long ride"
Within the cycling world there are definitely some people who are not keen on sportives. Quite a few traditionalists don't like seeing their sport invaded by newcomers who don't take cycling as seriously as them. Others think that the huge rise in the popularity of sportives will eventually lead to police officially regulating the events (and therefore making them much harder to organise) or insurers refusing to cover sportives following a major accident.
Some people say sportives should be classified as races - because they often have timing chips and publish their results - and therefore feel that they should get official permission to take place (and therefore there would be far fewer of them). This is not a view generally shared by British Cycling and the cycling authorities in continental Europe.