Algal bloom is a phenomenon where certain genera of algae (notably Alexandrium and Karenia) or cyanobacteria ("blue-green algae") reproduce explosively. When the species involved produce toxins, which often is the case, this makes the water unusable and possibly dangerous.
Although most such "blooming" species are microscopic, the concentrations are big enough to change the colour of the water and often give the impression of flakes. For cyanobacteria the result is green, for some algae red ("red tides"). It has been argued that one of the plagues described in the Bible where the Nile supposedly turned into blood, refers to an algal bloom, if the event is historic at all.
The bloom is a result of favourable conditions, such as large amounts of nutrients and suitable weather. It is not related to flowers, the species involved reproduce in other ways.
The involved classes of organisms are not necessarily harmful in general. Indeed, cyanobacteria are believed to have made the earth inhabitable for species breathing oxygen, and the chloroplasts in algae and plants (allowing them to use sunlight to produce nutrients) may have originated from a symbiotic relation with cyanobacteria.
Also pollen can accumulate in large quantities, and can then look quite similar to algal bloom, but is not harmful.
Water with visible amounts of cyanobacteria should not be consumed. Boiling does not help. Swimming in water with moderate amounts is not dangerous per se, but especially small children may accidentally swallow some water, so should be kept away. Animals such as dogs will try to clean themselves afterwards by licking, which will cause them to swallow significant amounts of the toxins. The water can also irritate the skin, so taking a shower, preferably with uncontaminated water, afterwards is recommended.
Some organisms consuming the blooming species, such as shellfish, may accumulate the toxins and thus themselves become poisonous.
In many places bathing in algae infected bodies of water is prohibited and you should heed the advice of local authorities, even though they might err on the side of caution in some places (and in others checks are done too seldom to be of any use).