Imagine a lone charged particle. It emits an EM field which propagates outwards at the speed of light.
If a charge would emit EM radiation, it would lose energy. In reality a charge obey a magnetic dipole moment and an electric field. Both are intrinsic (existing independently from outer circumstances) properties. They are static and nothing propagates outwards.
Now, let's say I hit the particle (with a neutral uncharged baseball bat) causing it to accelerate.
The baseball bat may be uncharged, but you over-give kinetic energy - usually associated with virtual photons - from the outer electrons of the bat to the charge. Since you are accelerate the charge, photons are emitted. After acceleration, a free charge moves without acceleration and doesn’t radiate. It has still its magnetic and its electric field.
Its EM field will move with it, overwriting the old one, creating a ripple in the field with propagates outward at the speed of light. An EM wave, also called light.
What are moving are the charges electric and the magnetic fields together with the electron. You can have this imagination, that during accelerations ripples occur. But the EM radiation always happens in quant, called photons. Under strong accelerations (braking is an acceleration too), you get “harder” photons like X-rays. Under soft acceleration you get photons more in the infrared or visible light.
My question is, how can this wave carry energy?
Simple the decrise in kinetic energy is accompanied by photon emission. QM treated a overall existing EM field in which photons are disturbances. But once again, the photons carry energy away.
Specially considering the particle itself didn't even have EM energy, since there is no other charge that could be affected by the light.
An acceleration is the reason for a charge to radiate energy. An acceleration could happens only in two cases. Or under the influence of other particles, like electrons, protons or even neutrons. Or under the influence of a magnetic field, called the Lorentz force.