It's easiest to demonstrate this template's use with a concrete example.

Say you want a nicely formatted link to Wikipedia:Manual of Style#Names and titles. You could use {{section link|Wikipedia:Manual of Style|Names and titles}} to give you Wikipedia:Manual of Style § Names and titles, but with this it is not very clear what the "Names and titles" section is referring to. {{Multi-section link}} solves this problem by allowing you to specify the intermediate section names, giving readers more context.

• {{multi-section link|Wikipedia:Manual of Style|Punctuation|Quotation marks|Names and titles}} → Wikipedia:Manual of Style § Punctuation §§ Quotation marks §§§ Names and titles