The length of time that contrails last depends on the humidity of the surrounding air and any wind. If there is high water vapour or ice content the trails can persist for many hours and can form fluffy trails or spread out and form sheets of cloud with natural cirrus clouds. If the air is dry then contrails tend to vanish rapidly. 

Contrails and climate change

Long lasting contrails have an effect on the climate, causing 1-2% of global warming (contrails.org). This happens when contrails spread and grow, trapping heat in the lower atmosphere. There are predictions that this could be significantly reduced by re-routing planes to avoid areas of the atmosphere with higher humidity, where contrails are more likely to form.

Chemtrails

There are theories that contrails are sinister – that they occur because governments, for example, are using aircraft to add chemicals to the atmosphere, either to affect humans (mind control, birth control) or as a form of geoengineering, to alter the climate. There are many problems with these theories. Always question any theory, and bear in mind that in many cases the more complicated an explanation, the less likely it is to be correct. It is very unlikely that any government could carry out such a large operation, involving so many pilots/chemists/engineers, without the truth being revealed. There is no evidence at all for chemtrail theories. As for solar or atmospheric geoengineering – this is a hugely controversial area of science, most research is still at the theoretical stage, and the risks (and costs) are very high. There are ongoing calls for a binding global moratorium on geoengineering, at the moment there is an agreement under the Convention on Biological Diversity that prevents geoengineering, with exceptions for small-scale scientific research studies (climatechangenews.com).