Consider a (diatomic) molecule undergoing an electronic transition. This transition is actually a band, comprising of a set of vibrational transitions. Each vibrational transition can be thought of being represented by distinct vibrational lines. This structure is then termed as the vibrational coarse structure. On resolving further on these distinct lines, it is revealed that each line is actually a cluster of many very closely spaced lines, thus forming the rotational fine structure. Within this fine structure, there lies a point at which the rotational lines pile up, and spacing between them goes to zero. This is called the band head.
For some reason, I had not heard of this term until it got asked me an interview. Actually, I think that’s likely not true, and I was probably told about, or explained to in my spectroscopy lectures. I just never remembered it, which is quite depressing. But at least I can change that now.