What are phonons actually? I was reading about heat conduction in solids wherein it was stated that in crystalline solids heat conduction takes place via lattice vibrations. In relation to this, the word phonon was used.
In radiation, the energy carried by electromagnetic waves as they move can be thought of to be carried in the form of small energy packets called photons.
Is this concept of phonons somewhat similar to photons? In the sense that, energy transport because of lattice vibrations can be thought of to be transported in the form of small energy packets called phonons? So that as these phonons move they carry the energy with them?
I interpret the concept of phonons as a sort of modelling to make things simpler to analyse. Am I right here?
P.S. - I'm studying mechanical engineering at undergraduate level, and initially posted this question on Engineering SE seeking  a rudimentary answer (most engineering textbooks on Heat transfer don't delve deep into this topic much). However, I was suggested to post this question here, with the reason that it requires deep understanding of something to explain it with a bit of simplification.
 A: 
Is this concept of phonons somewhat similar to photons? In the sense that, energy transport because of lattice vibrations can be thought of to be transported in the form of small energy packets called phonons? So that as these phonons move they carry the energy with them?

Yes on all counts.

I interpret the concept of phonons as a sort of modelling to make things simpler to analyse. Am I right here?

No, this is not correct. Phonons are not just a convenient model $-$ they are a distinctly quantum-mechanical phenomenon, and they lead to different predictions for several relevant physical quantities.
The idea of a phonon as a "small energy packet" is not bad, but it can be made more precise. A better way to think of lattice vibrations is that the configuration space of the motion of the lattice ions can be separated (via a Fourier transform) into a bunch of different modes with different wavelengths and different frequencies. A phonon is an elementary excitation in one of these modes. (But it is also possible for a phonon to be "spread" over a number of similar wavelengths, so it becomes a wavepacket with a well-defined location.)
The core idea is that the energy of the phonon obeys Planck's relation, i.e. it is given by $E=h\nu$ in terms of the Planck constant $h$ and the mode's frequency $\nu$. This quantization of energy then leads to different behaviour, the most famous of which is Einstein's calculation of the heat capacity once you account for this "lumpiness" in the amount of energy that can be held by each individual mode.
