The term Intonation in music means, put simply, producing notes that are in tune. It is what we would call śruti śuddham.
The most important factor for producing a note in tune is possessing an accurate outlook of that note. Once this is present, intonation is developed by practicing to match the note we produce with this standard.
In Carnatic music, of course, we do not have an "absolute note" -- they are all relative to the chosen reference ṣaḍjamam. Thus, for perfect intonation, a keen sense of hearing is absolutely essential.
When performing in large halls, musicians hear their own instruments only very faintly. And there isn't enough echo either. So, intonation becomes a big challenge.
Now, an accompanying Carnatic artist has a tougher problem -- he needs to be able to hear the main performer as well. Furthermore, an instrument that is initially tuned perfectly to the taṃbūrā, may go out of tune during the course of the concert; and the musician needs to be able to detect when this happens and correct it based on the taṃbūrā that is droning some distace away on the platform. This, however, is very rare with major artists and even more rare with smaller artists due to the efect of technology producing a shruthi box!!
Usually, to allow the performers to hear themselves, a speaker system that is directed towards the platform is provided. In addition, few concert venues are actually auditoria built with necessary acoustics for a music performance.
Given all these hurdles, I am amazed how our musicians perform with perfect intonation. They are practically performing deaf.
