The act of “reading ahead” (or “reading” or being “psychic”, or since the Japanese terms are somewhat popular for this kind of mind game, “sakiyomi” and “yomi”) refers to the art of predicting one’s opponent’s actions. It also refers to (one’s own) actions that exceed said actions.
This is not the same as “shenanigans” (e.g. exploiting one character’s weakness only because you can guess there’s a very good chance your opponent won’t do the one thing it will take them to escape it – but you don’t really know), which may well be considered part of a good gameplan, but usually only carry the connotation of being cheap (see also: checkmate). Truly using moves “psychically” carries the connotation of cunning, highly-trained skill, and possibly impressive reflexes.
Being able to read ahead is not an absolute requirement for success in battle all the time (as opposed to having a good gameplan, having combos prepared, and just being well-attuned to your playing in general), but having some bit of reserve and reaction is what it takes to be able to fight, so it is an essential component of good gameplay.
In particular, basic anti-air and stuffing do need some degree of reading ahead.
The trick to not being read is to avoid sticking to a predictable pattern. An opponent who follows no true pattern is basically impossible to read.