Bedbugs are small creatures that like to hide and proliferate in environments where humans or any other warm-blooded animal is present. Often, as they travel with people from one hotel to another, they find their way into our homes. They can be found in the folds of the mattress, in the wood of the bed slats and even in clothes.
Although they are very small animals, the bites are easily recognisable. Initially they look very much like those of a common mosquito, except that they are often in groups of 3, all in a line, because adult bedbugs sting 3 times and move very little.
National Geographic, in this regard, has published a very nice (and a bit disturbing...) video that effectively shows everything you need to know about bedbugs. You can see it by clicking here.