Binary ``=~'' binds a scalar expression to a pattern match. Certain operations search or modify the string $_ by default. This operator makes that kind of operation work on some other string. The right argument is a search pattern, substitution, or transliteration. The left argument is what is supposed to be searched, substituted, or transliterated instead of the default $_. When used in scalar context, the return value generally indicates the success of the operation. Behavior in list context depends on the particular operator. See Regexp Quote-Like Operators for details.
If the right argument is an expression rather than a search pattern, substitution, or transliteration, it is interpreted as a search pattern at run time. This can be less efficient than an explicit search, because the pattern must be compiled every time the expression is evaluated.
Binary ``!~'' is just like ``=~'' except the return value is negated in the logical sense.