Supernatural or Inter-dimensional?
SPOILER ALERT! If you haven't watched "Bird Box" yet, don't read until you've seen it.
Now that we've got that out of the way, the creatures had to have been either supernatural or inter-dimensional. As mentioned by a previous poster, the movie has elements of "A Quiet Place" and "The Mist." At the same time, the movie is completely different in that it takes on the supernatural aspects of an apocalyptic scenario when Charlie address the folklore of various religions and when Gary lays out the pictures of demonic looking beings on the table. These are subtle hints as to the nature of the creatures.
If they are demons (supernatural beings), then I find it interesting that no one ever stops to have a group discussion about what (if any) religious defenses they might try to use against them. They obviously want to do harm to the living and the ways people kill themselves is usually ghastly. This conveys a nature of malice.
If they are inter-dimensional (time/space beings), they could be creatures that feed off the energy of extreme fear/psychosis/euphoria and deplete that energy quickly by killing off their hosts. This would make them parasitic in nature. However there's a wrinkle with that explanation and that's the people the creatures keep alive to do their bidding, such as Gary and the roving killers that Tom puts down at the house. The creatures can obviously not kill people they attack all the time, so that shows a more deliberate intelligence. In nature, some varieties of parasites will keep a host alive for a while, if it's beneficial to them. This conveys that perhaps the creatures aren't so much evil as they are opportunists.
Some hints of answers in the movie but very little to go on. Guesswork here.
Other thoughts?