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Footnote Functionality
Footnotes provide additional information or references for a body of text. In Obsidian, a footnote has two parts: a footnote reference (the [^1] in your text) and a corresponding footnote definition (the [^1]: ... line that holds the footnote's text).
Footnote names can be numbers or words ([^1], [^smith2024], [^注]), but they can't contain spaces, tabs, backticks, brackets, or #: Obsidian can't render or find such footnotes, and the plugin refuses those characters.
In Obsidian (and other Markdown editors), the name only says which reference belongs to which definition. In Reading view, every reference and its definition are numbered in order of appearance, whatever you named them.
Source mode:

Reading view:

Obsidian also lets you create inline footnotes by typing the following:

Inline footnotes can contain spaces. In Reading view, they are gathered at the bottom of the page alongside the other footnotes.

The plugin's Insert inline footnote and Insert inline footnote from clipboard commands write them for you, and a second press of the inline hotkey hops the cursor out past the closing bracket. See the README.
A footnote reference inside code, math, a comment, the frontmatter, or another footnote's definition would not be a footnote to Obsidian, so the plugin refuses there and tells you why. A [^1]: line typed directly under a paragraph, with no blank line above it, is plain text to Obsidian too; the plugin's linter inserts the missing blank line (the Fix definitions hidden by a missing blank line rule) or alerts you about it.