Blue-green algae is the commonly used named for cyanobacteria, and a literal description due to the recognisable blue and green colouring you will notice looking at them, either through a microscope or by seeing them in large quantities, in which case they tend to form greenish flakes.
They are essentially single-celled organisms (although there are variants) commonly found in fresh water, where they float freely or colonise rocks and surfaces. They are part of the natural environment and contribute to their local ecosystems by photosynthesising and producing substances that support the food chain. They can pose a problem in water when they multiply too much, causing the water to turn green which blocks sunlight from getting to plants and creatures.
When blue-green algae gradually form scum or bloom, this can actually produce toxins and in significant quantities these can cause other issues. Under some circumstances, cyanobacteria can explosively reproduce and quickly become a widespread problem. Harmful algal blooms can kill wild animals, farm animals and pets if consumed, and in humans the symptoms are more commonly skin rashes and other minor illnesses if ingested. Not all cyanobacteria will produce toxins and some are harmless, but since it’s impossible to see the difference it’s best to assume all are poisonous.
On the other hand, under different circumstances, blue-green algae have been found to have potential health benefits too. It’s possible to buy them in the form of tablets, which are used to treat a variety of issues. In some cases they have been shown to help stabilise the immune system, fight tumours, reduce inflammation, plus have a positive effect with cases of herpes, hepatitis and even HIV.
The research done so far has been enough to draw conclusions under certain scientific conditions, hence the uses of blue-green algae have been varied so far, but the extent to which we can benefit from or suffer from the bacteria remains to be proven.