At the microscopic or molecular level you have electronic transitions and molecular transitions. Electronic transitions for example the electron is excited to a higher energy level. In a molecular transition the molecule in a spring model (bonds like springs between atoms - phonons) the molecule gets excited to a higher mode of vibration. For electronic transitions they are often in the visible spectrum, molecular transitions they are in the infrared, or far infrared. You can also look at semiconductors where instead of discrete energy levels you have different energy bands. Usually we talk about a conduction band or a valence band, but there are higher empty bands that electrons could get excited to, or when an electron is excited to conduction band it may be excited to a state that is not at the minimum energy of the conduction band. For metals the absorption might be from collective oscillations of electrons called plasmons.
Anyway the point is that if you look at it from an energy level perspective and you excite to a higher level. The absorption excites the particle (electron, phonon, etc.) from a lower energy to a higher energy and you could have re-emission from that energy state, but often there are other processes where that particle loses energy through other processes before it can re-emit.
That loss of energy typically ends up in the form of heat, but if you wanted to look at it from a particle point of view that "heat" might be a phonon vibration that goes through the lattice.
If it was a solar cell - sometimes you might thing of this as a loss of efficiency, a high energy photon comes at 2.5 eV, but the band gaps of the silicon is about 1.1 eV, the photon gets absorbed losing 2.5 eV, when the electron rattles between allowed states down to the bottom of the conduction band it only has about 1.1 eV - so about 1.4 eV was lost in the form of heat. Silicon is also not very good at emitting light so it doesn't lose that energy in the form of an emitted photon.
If it was something like a dye molecule in a liquid and you illuminated it with visible or UV light, it might very efficiently emit photons between some energy levels, but usually that emission will be substantially longer wavelength than the exciting photon, and the difference in energy is going somewhere by vibrating the molecule or being transferred by molecule to molecule collision to the liquid solvent. Or if the dye molecule doesn't emit in the form of a photon it is heated up.
So if visible light from the sun - black body spectrum about 5700k some gets reflected, some gets absorbed, some might be remitted as photons at lower energy, but in general what absorbed is heating up the material and that material is at a lower temperature say 300K and radiates with a black body spectrum around 10 um. If the sun heats it up to 310 K, then the peak of the spectrum would emit at a slightly shorter wavelength.
Since materials can be complex it is often convenient to measure a emissivity or absorptivity when discussing how well the material emits absorbs or emits the thermal radiation.