This is a condition where there is a small bleed from a tiny blood vessel beneath the clear membrane that covers the white part of the eye. Since the membrane is clear, and the space beneath it is small, the blood spreads and is highly visible and dramatic in appearance.
In the vast majority of cases, this is spontaneous and harmless. The blood clears over a period of a week or two, gradually turning yellow and disappearing.
Subconjunctival haemorrhage can be indicative of other bleeding disorders such as those induced by drugs e.g. Aspirin or Warfarin. If you are on Warfarin it would be prudent to get bleeding times checked. You should have your blood pressure checked.
If the haemorrhage is occurring in the presence of haemorrhages elsewhere, this should be investigated.
Similarly if the haemorrhages are occurring in the context of a change in health such as weight loss, fever, or generally feeling unwell, this needs investigation.