If the gravity was half as strong, how would the enviroment change? Would all the plants grow differently? What change would there be in flying creatures?
Gravity plays an important role not just on how life forms evolve, but also on the evolution of the planet itself. The gravity of a planet or moon is a property of its size and density; thus a body might have the same gravity as that of a smaller, denser one.
If the Earth had half the gravity it does now, it's possible that life would not have evolved, due to a thinner atmosphere, and a host of other consequences resulting from that one change alone.
Other factors affect whether a planet's atmosphere is conducive to life, how well protected it is from solar winds, and how well the atmosphere retains or sheds heat. Things like the distance from its star, the period of the planet's rotation, its magnetic field, and so on. You could conceivably balance these factors to explain how a planet with much less gravity has a habitable atmosphere.
In the question Can you simply scale up animals?, it is explained that the square-cube law prevents things from becoming too large; as the size of an animal increases, its volume (and weight) increases much faster compared to linear measures such as height. Reducing gravity would not change this law, but it would change the boundary where its effects cause organisms to be unable to grow larger.
For example, the largest living land animal today is the African Bush Elephant, averaging just under 5 tons and standing about 11 feet tall at the shoulder. With half as much gravity, it would not be unreasonable to think such an animal could be twice as massive. Working backward from this, it would be like adding about 25% to its height and length. In other words, scale the elephant up to stand 13.75 feet tall and its mass would double from 5 tons to 10 tons. With half as much gravity, its weight would be the same, but its larger dimensions would be proportional to the new gravity.
This is of course just a back of the envelope calculation. Larger animals have existed in prehistory, like the truly immense sauropods, the largest of which might have been 135 tons and 30 feet tall. With half the gravity, it could have been almost 38 feet tall instead.
This same question came up on Quora, where answers agree that plants would likely be much taller (though there are counter-examples). With less gravity, flying insects and birds might need less muscle power, but with thinner atmosphere, also need larger wings for more surface area to push against.
Consider that small animals and insects can fall without getting hurt (the square-cube law working in reverse). The size at which this is possible would be larger. Imagine how high a cat could leap from the ground to a building ledge. A typical house cat can leap about 5 feet, or five times their height. Although you might think that in half gravity this could be doubled, remember that muscles would have evolved requiring less mass to overcome gravity's effects. So I would probably estimate the low-gravity version of a house cat to be able to jump somewhat less than ten feet.
There are many other tradeoffs, the likes of which I am not sure about the calculations for. For example, the escape velocity from the planet would be less, so rockets would not need to be as bulky. However, energy production from hydroelectric dams might also be less, because gravity (after all) is what pulls it down through the turbines.
It would be relevant what causes the gravity to decrease, and also how quickly the change occurs.
Assuming gravity isn't going down because much of the matter inside the planet is vanishing, and/or somehow the gravity is going down without causing massive instability in the planet's crust (which I imagine it would - I think there would be massive earthquakes and volcanic eruptions):
Some large buildings I think would be in trouble, while others might not. In general, I think it would reduce much of the difficulty in standing up that structures are designed for. On the other hand, it would change the forces at work on practically everything, and that might lead to things cracking and breaking. If there are objects not being pushed sideways partly because of the friction in response to their weight, they might slide out of place. Some things might creak and groan and break, and others might fall down, but I think in general most buildings would be more stable.
If no other disaster came with it, it would seem to me very fun to jump around in half gravity. Boing, boing! You could throw things higher and farther, too.
The atmosphere of the planet would I think be in danger, I expect catastrophically, but I'm not certain. Astronomers talk about Mars having had insufficient gravity to hold its atmosphere, so I think that's the worst problem, but reducing air pressure itself (it would go down by 50% even without losing any air) would have health effects. The atmosphere also has a lot to do with temperature on the planet, so that would also be awful for existing life forms.
If somehow the only changes was the gravity, then plants would be able to grow taller.
Flying animals and aircraft would be much more capable of flying from the lack of gravity, except if the air pressure went down, that would make it much harder to fly using wings or rotors or jets. I'm don't know what the effect curves look like. Rockets on the other hand, would have a much easier time with lower gravity, and thinner air would help them too.
If halving the gravity results in halving the atmospheric pressure, you will push most humans right up against the death zone, it would be as if the people at sea-level were all living at around 5,000 meters, which is about the highest recorded permanent human settlement.