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"Millimeter" refers to the wavelength of light. "Continuum" is a shorthand that in this context refers to thermal emission.

All matter emits thermal radiation. The spectral energy distribution of this radiation is determined by the Planck's law [1]. If you measure the spectrum of an object, some part of it will be from this thermal emission, which is a continuous function of wavelength/frequency. In many cases, the conditions are right for spectral lines [2] to be produced, either in emission or absorption. Because these features are centered at specific wavelengths, they are not usually thought of as "continuous" features in the spectrum. (This isn't strictly accurate, as all spectral lines suffer some broadening into extremely narrow, but still continuous, features. Additionally, there are sometimes finite width continuous features called "bands" that arise due to so many lines being present that they blend together.) Generally the continuous part of the spectrum is called "continuum" while the other parts are "lines."

[1] https://en.wikipedia.org/wiki/Planck%27s_law [2] https://en.wikipedia.org/wiki/Spectral_line