Why do batters need resting?
Two things happen while a batter stands, and both improve the result — which is why the instruction appears in recipes for pancakes, Yorkshire puddings, crêpes and batters for frying.
Gluten relaxes. Mixing flour with liquid develops gluten — protein strands that give structure but also elasticity. A freshly mixed batter is tight and springy, which makes pancakes tough and rubbery and makes crêpes contract in the pan. Standing allows those strands to relax, producing a more tender result and a batter that spreads properly.
Starch granules hydrate fully. Flour particles absorb liquid gradually. Immediately after mixing, much of the starch is still dry in the centre. Given time, the granules swell completely, which thickens the batter — frequently noticeably, so a rested batter may need thinning — and produces a more even texture. It also allows lumps to dissolve on their own, which is why vigorous whisking to eliminate lumps is unnecessary and actively counterproductive, since it develops more gluten.
Air bubbles from mixing also disperse, which matters for even cooking.
How long. Thirty minutes makes a clear difference; an hour is better; and overnight in the fridge is common for crêpes and Yorkshire puddings. Beyond a day the batter can separate, though it can be re-whisked briefly.
Where it matters most:
Crêpes and thin pancakes, where toughness and contraction are obvious.
Yorkshire puddings and popovers, where a rested batter is widely held to rise better.
Beer batter and tempura — with an important exception: tempura is deliberately not rested, and is mixed minimally with very cold water and left lumpy, precisely to avoid gluten development and keep the coating light. Resting would work against it.
Where it matters least: thick American-style pancakes raised with baking powder, where the raising agent begins working on contact with liquid. Resting these too long wastes the lift, and the rule is essentially reversed — mix lightly and cook promptly.
The related principle applies to pastry and pasta dough, which are rested for the same gluten-relaxing reason.