The confidence estimate represents how sure the site admin is, that the element's actual atomic spectrum visually resembles the generated lines image on your screen, based on such considerations as the ability to obtain a high quality photo; the similarity of line intensities in the two data sources; the energy level diagrams of the element; the "believability" of the source intensities compared to similar elements with well photographed spectra; as well as the ability to get a good direct visual observation of the spectrum.
This confidence estimate applies only to the overall visual appearance of the element's spectrum, and does not necessarily indicate confidence in the intensities of individual lines, particularly in complex spectra with hundreds or thousands of lines, or spectra where many lines may appear to be one line or one "stripe" in visual observations and/or photographs.