Assume: Current humans, in their current form, on an Earth with somewhat less gravity. Say .75g
We would jump a third higher.
Be able to lift a third more.
Climb a lot easier.
Be a bit more clumsy, because inertia and weight will feel mismatched.
Fall more often, but not quite as badly, because of the same clumsiness and reduced traction, but slower running and falling speeds.
Walk further before exhaustion, as walking requires less effort.
Run slower, because inertia is the same but traction and ground contact time are reduced.
Pretty soon, our muscles will atrophy to the point were all but the last item are nulled out.
Assume: Humans, with normal genetic heritage, but born and raised on a lower-gravity Earth.
Will grow quite a bit taller on average.
Will have slightly worse reflexes, simply because they are never trained at the same pressure as under full gravity.
Will walk faster, because of less effort by fully acclimated and longer legs.
Will run slower, because with the taller bodies they will likely mass even more, but still have less traction.
Will jump.... about the same? Possibly a bit higher. They have longer legs, and need to fight less gravity, but will have more mass to hoist and weaker muscles to do so with.
You also ask about water.
Water is gravity in motion.
With less gravity, water will flow slower and fall slower, in direct proportion to the reduced gravity.
Waves will be higher but slower. Again, in direct proportion to the gravity for speed, and roughly inverse squared gravity for height. (1/2 gravity makes for 3-4x as high waves, moving half as fast)
Trees would be much taller, as they both require less trunk strength to lift the tops, and capillary effect would be able to lift water higher, easier.
If you actually edit the Earth's gravity, remember that effective air pressure is the direct result of the weight of the air in the atmosphere above you.
If you halve the gravity but leave the atmosphere untouched, you will also have half of the sealevel air pressure. Which will soon kill almost every insect and mammal in sight. (it's equivalent of 18000ft altitude)