What is dark matter?
What are the effects of both dark matter and dark energy?
Nobody knows exactly what they are which is partly why they are called 'dark'.
They both are observed indirectly by their effects but the cause is unknown.
In the case of dark matter something unseen is causing gravatitational effects so it has to be some kind of matter.
It's widely suspected to be some kind of subatomic particle which has so far not been detected.
That is not the only theory, but experimental work is in progress to try to detect such particles.
Dark energy is even more mysterious. Something seems to be causing the Universe to expand,
(although that is in the large scale, individual galaxies are not expanding, but generally galaxies are moving away from each other)
So does dark energy exerts some kind of anti-gravity?
You could think of it as a force which works as an opposite to gravity, but only on the very largest scale.
At the scale of stars and planets it is insignificant,
Not any more-so than magnetic levitation would be anti-gravity. When gravity pulls two objects together, they move through spacetime to get to each other. When dark energy pushes two objects apart, it does so by literally adding more space in between them.
This is a common heuristic viewpoint, but you should be aware that it has significant limitations. This came up in another thread just now, see here:
Dark energy and expansion vs gravity and spatial contraction
Just to clarify a bit, the universe is expanding and will continue to do so without interference. Observations uncovered the surprising fact that the expansion seems to be accelerating, which was unexpected. We would expect gravity to slow down the expansion instead. We have no idea what is causing the accelerated expansion, but have given it the handle of "dark energy," which sounds more dignified than "spooky expansion pushy stuff." We don't even know if it's energy. We are at the level of a cave man finding a nickel-iron meteorite and thinking it is just another rock.
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