<meta charset="utf-8"> declares encoding of own file?

Until this element is read, the document is interpreted with the default encoding of the user agent. (This is often ISO-8859-1.) If the encoding is different from the default, then the document is re-interpreted according to the meta element. That's why you should place it as early as possible in the body, or preferably use an HTTP header (see below).

The hope with the <meta> element is that the preceding characters are all in the ASCII character set, which are interpreted correctly in just about all character sets.

In general, however, and if it is possible, this information should be sent in an HTTP response header:

Content-Type: text/html; charset=utf-8

This ensures that the document is interpreted correctly from the start.

It's true that it's paradoxical for a document to declare its encoding within itself. And it really is only a secondary fallback. The HTTP Content-Type header always takes precedent if set; and it should always be set.

Declaring the charset in an HTML meta element makes sense in case the document is ever treated in a non-HTTP context; meaning if it's ever not served over HTTP and can hence not declare its encoding in the HTTP header. This may be the case if the document is downloaded and saved for later offline use. In this case it just so happens that most encodings are ASCII compatible, and the browser will typically try to read the document in an ASCII compatible default encoding like Latin-1 or UTF-8 (depending on the settings of the browser) until it encounters the meta tag. If your document is saved in a non-ASCII compatible encoding, say Shift-JIS or GB18030, this may or may not work depending on the default settings and how intelligently the browser can figure out what encoding it's dealing with; it's really mostly up to the browser how to deal with this situation.