An emulsion is two liquids that don't want to mix — fat and water — forced into a stable suspension by an emulsifier and mechanical energy.
Lecithin molecules have one end that bonds with water and one end that bonds with fat. Temperature is critical for warm emulsions like hollandaise — egg yolk proteins begin to set around 65C, but above about 70C those proteins coagulate and you get scrambled eggs in butter. The window is narrow.
If your hollandaise breaks, start a fresh yolk in a clean bowl with a splash of warm water, then slowly whisk your broken sauce into it. Always start thick, then thin to your desired consistency.
Adding fat too fast — the single most common cause of a broken emulsion. Too much heat on a hollandaise, scrambling the yolks. Starting with cold yolks.