Fossils show that during the Earth's Late Carboniferous period (around 300 million years ago) there were several species of insects - e.g. Meganeura (giant dragonflies) and Arthropleura (giant millipedes) - which reached sizes far larger than known today.

There are currently (at least) three theories regarding the phenomenon. See : Wikipedia

The upper limit on insect size is generally assumed to be associated with the way in which they 'breathe' through absorption. After a certain size limit, they would not be able to absorb oxygen fast enough to operate efficiently.

As early as 1911, theories were proposed suggesting that there may have previously been more oxygen in the Earth's atmosphere - roughly 10-15% higher than today, which would have allowed insects to grow much larger than is currently viable.

Another theory suggests that they may not have had many (or any) predators, and this allowed them to grow. Many of today's largest animals have very few, if any predators.

The third explanation is that water-dwelling larvae had to grow bigger in order to protect themselves from toxic levels of dissolved oxygen in the water. See : PLOS ONE, 2011

As yet, however, there is no generally accepted explanation.

( Note that there are many other fossil records of 'Gigantism' - an example from an earlier period is a water-dwelling arthropod called Jaekelopterus rhenaniae, which is thought to have reached 2.5m in length. ref.)