Weather Satellites
There are two types of satellite that take weather images, geostationary and polar orbiters

These are located at about 36,000 kilometres above the equator. 
The orbit time is 24 hours exactly, so they effectively remain at the same point over the Earth's surface. 
The ones that interest us are the Meteosat series which are over the equator at approximately 0 longitude.
Some websites provide animations over the past few hours 
(more about this later)
They can take pictures at any time of day or night. 
(every 15 or 30 minutes)
Resolution is limited because of the distance of the satellite.
Moreover, the image is distorted due to the angle from which it is taken
Some providers modify images to reduce distortion.
Images from geostationary satellites can be available within 15 minutes of the picture being taken
Polar orbiters
These fly 800 kilometres above the surface so give high resolution images. 
They make 14 orbits per day (approx 1 hr 42 mins each orbit) passing close to the poles. 
Between one orbit and the next, the earth has rotated ~ 25. 
Thus they are only able to look at the British Isles during two consecutive orbits and then there is a gap of over 10 hours  before they can look at us again and therefore take only four useful images each day of a particular place.
first passnextpass
Polar satpics images might not be available for several hours after the pass so are best used to see what happened, ie for 'de-briefing'.

High resolution Polar Orbiter visual images can distinguish features as small as 250 metres, so will show individual cumulus.

Both types of satellites can take visual and infra red pictures
Visual images are in effect straightforward photographs (some are given false colour to improve the presentation).  However, they can only be taken during daylight. Infra Red are available throughout the day and night.  The sensors (indirectly) measure temperature.  Infra Red suffers from several disadvantage - the temperature at the tops of low cloud or fog can be very similar to the surrounding clear ground, so overnight fog or low stratus does not show up very clearly.
TIP for capturing images when "Save Image" does not work.  On top row of keyboard, press "Print Screen" 
This is a misnomer.  It should say "Grab Screen". 

Then paste in to your favourite image processing program, crop and edit as required.
Links to examples
Polarvery high resolutionB Burton with archiveweatheronline
Geostationaryhigh resolution every 3 hrsMet Office visualMet Office infra red