In the Astrobites article Spectral Line Survey Reveals New Molecules in Two Protoplanetary Disks integrated emission maps depict the spatial distribution of the flux received from each "line." I am unsure as to what this line is, nor do I know what the x and y axes represent in terms of interstellar molecules' emissions. Do the x and y axes just represent the position and velocity of the molecules in a galaxy?
Those are plots of the real spatial distribution of flux at certain frequencies, as it appears on the sky.
The latter can be seen as the x-y axis in each individual plot refer to the declination and rectascension ($\alpha-\delta$), i.e. standard celestrial coordinates.
The link provided in a comment has a plot of the spectrum of the two discs:
Such a 'total spectrum' for the objects shows various molecular footprint lines in emission (LkCa 15 is inverted, hence those are emission lines as well). A line is hence simply the sharp emission peak that molecules emit at those energies (here those are rotational lines, but vibrational and electronic modes exist as well).
Now to get a better understanding where in the disc those molecules sit and how strongly they are concentrated, ALMA is able to measure the spatial flux distribution at a very sharp frequency, generating the above images.
They are called integrated emission maps, because you have to do a longer time-integration (10-30 mins) to get each of them. They also pose a fantastic tool for us, as as long as the emission is optically thin, the total flux is proportional to the total number of molecules, hence one can determine absolute numbers with those measurements and learn about the early chemistry in protoplanetary discs.