An encoding is simply a mapping between numerical values and "characters".
US-ASCII maps the number 65 to the letter A, 32 to a space and 49 to the digit "1". (How these things are rendered is another matter.) In fact, UTF-8 does the same! But there are other values which UTF-8 treats differently to ASCII. It is a variable-length encoding, i.e. a character may be encoded with 1, 2, 3, or 4 bytes; common characters generally consume less bytes.
Plain text files, including web pages, are stored and transmitted as sequences of bytes. These bytes are supposed to represent something textual. Software applications (like text editors and web browsers) are responsible for rending the information within these files on the screen. Usually they make use of library or OS functions.
If the software assumes a different encoding to the software that created the file, the wrong characters may be displayed!
Note that it is possible to convert between different encodings; however if you convert to an encoding that does not contain a certain character, the software must make a choice as to what to use instead. This conversion often happens transparently (when you save a file with a certain encoding, whatever you've typed must be changed into that encoding).