The does not contain operator allows you see if a text field does not contain a piece of text. The text can either be an unquoted single value, or a quoted value (in either double or single quotes) - normally you would use quotes around the string to make it clear you are searching for text.
The contains value supports the Lucene Query parser syntax as documented here
Text is indexed using the "Standard Analyzer" - this means that common words such as "a", "the", "this" etc. will not be indexed.
To return all values that do contain some text, use the Contains(!~) Operator.
Any records with a name not containing the word Test:
Name !~ Test
Any records where the name does not contain either "defect" or "bug"
Name !~ "defect bug"
An records where the name does not contain the value:
Name !~ "'change password to invalid value'"
Any records where the name does not contain any word matching the single letter wild card (would exclude records where the field contains the text, test etc):
Name !~ "te?t"
Any records where the name does not contain a word start with the text "log" (would exclude log, logging logged etc.)
Name !~ "log*"
Long-hand form of the operator:
Name DOES NOT CONTAIN "log"
There is a special field Text which you can search against will expand to search against all fields support the operator "does not contain".
Here is example of it's usage to find any records where they contain the text "exception":
Text !~ "exception"