Everything in a biological system has a biological half-life, that is a measure of how long it will stay in that system until it is lost, excreted, degrades, reacted into something different, etc. Most substances have a short half-life, as they are metabolized, or excreted as waste.
However, some compounds may stay in a system for a much longer period of time. For example, calcium in the human body is laid down in bones and teeth, and even when bone cells die, their calcium is used again in the building of bones. This is a sensible and efficient re-use of scarce resources.
The problem arises when toxic substances stay in the body for a long period of time. They are not acutely poisonous, otherwise they would kill straight away, but are associated with chronic poisoning.
If the input of a toxic substance to an organism is greater than the rate at which the substance is lost, the organism is said to be bioaccumulating that substance. Thus, the longer the biological half-life of the substance the greater the risk of chronic poisoning, even if environmental levels of the toxin are very low.
This is one reason why chronic poisoning is a common aspect of environmental health in the workplace. As people spend so much time, for so many years in these environments, very low levels of toxins can be lethal over time.
An example of poisoning in the workplace can be seen from the phrase "as mad as a hatter". The process for stiffening the felt used in making hats involved mercury, which forms organic species such as methyl mercury, which is lipid soluble, and tends to accumulate in the brain.
Other lipid (fat) soluble poisons include Tetra-ethyl lead compounds (the lead in leaded petrol or gasoline in the US).
Strontium 90, part of the fallout from atomic bombs, is mistaken by the human body for calcium, and is laid down in the bone, where its radiation can cause damage for a long time.
Naturally produced toxins can also bioaccumulate. The marine algal blooms known as "red tides" can result in local filter feeding organisms such as mussels and oysters becoming toxic; coral fish can be responsible for the poisoning known as ciguatera when they accumulate a toxin called ciguatoxin from reef algae.
Other compounds that are not normally considered toxic can be accumulated to toxic levels in organisms. The classic example is of Vitamin A, which becomes concentrated in carnivore livers: Polar bears are the classic example: as a pure carnivore that feeds on other carnivores (seals), they accumulate extremely large amounts of Vitamin A in their livers. It was known by the native peoples of the arctic that the livers should not be eaten, but Arctic explorers have suffered vitamin A poisoning from eating the bear livers (and there has been at least one example of similar poisoning of Antarctic explorers eating huskie dog livers).