There are many theories about why polar bears were on the island.
The first theory was that Dharma brought polar bears to the island to manipulate their genes so they could adapt to warmer temperatures. Some believe evidence of this is contained on the Blast Door map which stated "STATED GOAL, REPATRIATION ACCELERATED DE-TERRITORIALIZATION OF URSUS MARITIMUS THROUGH GENE THERAPY AND EXTREME CLIMATE CHANGE." If Dharma was concerned about "the end of the world" through global collapse of the environment, it could have been looking to find a way for animals and humans to adapt to the massive eco-disaster as foretold by the Valenzetti Equation.
However, the gene experimentation on the polar bears seems weak considering that most American zoos have polar bear exhibits in climates well above the natural Arctic habitat.
The second theory was that Dharma was using polar bears to train them to do certain tasks. When Sawyer and Kate were locked up in the cages, Mr. Friendly told them the bears took little time figuring out how to receive fish biscuits from the cage machine.
Dharma was training polar bears to turn the frozen donkey wheel in order to move the island. The evidence of that is the polar bear (with Dharma dog tag) skeleton found in the Tunisia desert, around the same place as Ben wound up after he turned the frozen donkey wheel. We can assume that the early Dharma folks were concerned about the energy fields, as it killed at least one worker in the Orchid station. As a result, the science team conditioned the polar bear, a strong animal, to move the donkey wheel so as not to risk human life. Polar bears were chosen because they could tolerate the cold chamber where the wheel was located (which in itself is contra-indicated because the deeper one goes below the surface of the earth, the hotter it would get). But after some time, the concern over humans using the donkey wheel must have subsided as both Ben and Locke turned it and wound up okay in the desert halfway across the globe.
A third theory is more simple: polar bears were brought to the island to mess with visitor's minds. Dharma was all about mind control (see, Room 23). What is more disorienting to a visitor in a tropical jungle than being confronted by a large polar bear? The expression on Sawyer's face was priceless when he was firing rounds at the charging polar bear. It also brought to the the first major mystery, as spoken by Charlie to the fans, of "where are we?" This mystery of what was the island; where was it located; and what was its purpose is still unresolved.
But some may consider the polar bears as another writer twist of throwing something that should not belong in the normal course of events. It is a prop designed to confuse viewers with the aura of mystery but with no answers forthcoming (i.e. the theory that the writers were just making up things as they went along to keep fan interest whether it made sense or not).
The polar bears could also symbolize the main characters: people who were out of their normal place, being manipulated by forces unknown to them, and losing control over their own lives.
