Mordanting is the process of adding a soluble metal to the fibre, which aids the dye in adhering to the fibre.
Almost all natural dyes are not substantive and require the use of a mordant. The most common mordant is alum (potassium aluminum sulfate) a food safe ingredient that used in pickling, which gives a clear bright shade.  Another common mordant is iron, which darkens or "saddens" the shades.
Cochineal, Osage, Logwood and Madder all require the use of a mordant.
If you are dyeing cellulose or plant fibres such as cotton, you also need to pre-treat your fibre with a substance that is high in tannins. Our favourite is gallnut, which leaves the fibres clear and bright.
If you are using a protien or animal fibre such as wool or silk, you need the metal mordant (such as cotton), but you can skip the tannin step.
If you are dyeing with indigo, your fibres do not need to be mordanted.  However, indigo is also not substantive and must be dyed by creating a vat, using an alkali and a reducing agent.