For example, the proton beams in the LHC collider have 7 TeV energy. Does this mean that the individual protons in the beam have 7 TeV energy or that the energy of all the protons in the beam add up to 7 TeV?
In the LHC, each individual collision has a center-of-mass energy of roughly 14 TeV. Since the collisions are symmetric (two protons with equal energy, moving in opposite directions, collide), we can say that each individual proton has roughly* 7 TeV of energy.
As you can probably tell, adding up the energy of all of the protons in the ring at any given time gives you a pretty colossal amount of energy.
*In reality, there's a distribution of energies that the protons in the beampipe can have, due to the fact that accelerators can only be so precise.The distribution is centered around 7 TeV, and is sharp enough that we can safely talk about collisions having a pretty uniform center-of-mass energy in most cases.
Collision experiments are done to create particles that can not be studied under normal circumstances. Energy and momentum conservation as well as the famous Einstein equation $E=mc^2$ tell us that a heavier particle can not just "pop out of thin air". But if we let two particles with enough energy collide, they can create a new particle, if the incoming energy is high enough. Therefore the individual particles in the collision beam need to have a high energy.