Spectroscopic constants - explanation
You can find plots and further explanations online (as I easily did). This is a homework-type question, yet I do feel that the information request for diatomic molecular spectroscopic constants warrants at least this partial answer. See this writeup for the "Vibronic Absorption Spectrum of Molecular Iodine" for more details and illustrations.

From NIST:

T$_e$ minimum electronic energy (cm$^{-1}$)

R$_e$ internuclear distance (Å)

ω$_e$ vibrational constant – first term (cm$^{-1}$)

ω$_e$x$_e$  vibrational constant – second term (cm$^{-1}$)

B$_e$ rotational constant in equilibrium position (cm$^{-1}$)

α$_e$ rotational constant – first term (cm$^{-1}$)

D$_e$ centrifugal distortion constant (cm$^{-1}$)

β$_e$ rotational constant – first term, centrifugal force (cm$^{-1}$)

From Wikipedia:

D$_0$ dissociation energy (cm$^{-1}$)