How do molecules having speeds many times greater than mean speed help in making nuclear fusion reactions in a laboratory?
Nuclear fusion is a process in which two or more nuclei are combined to form a different atomic nucleus.
It takes a lot of energy to force nuclei to fuse, even with the lightest elements, like hydrogen in the Sun.
Now the release of energy and the fusion iself goes down between two forces:
strong force (residual strong force, that is the nuclear force), that keeps the neutrons and protons together
EM repulsion, that keeps protons away
When you accelerate nuclei to high enough speeds, they can overcome this EM repulsion, so they can be brought close enough, where the nuclear force is strong enough to hold them together.
At large distances, two naked nuclei repel one another because of the repulsive electrostatic force between their positively charged protons. If two nuclei can be brought close enough together, however, the electrostatic repulsion can be overcome by the quantum effect in which nuclei can tunnel through coulomb forces. When a nucleon such as a proton or neutron is added to a nucleus, the nuclear force attracts it to all the other nucleons of the nucleus (if the atom is small enough), but primarily to its immediate neighbours due to the short range of the force.