Time -Domain to Frequency Domain
By convention they mean the following:

$x(t)$ = Input in the time domain

$h(t)$ = Filter impulse response (time domain)

$H(w)$ = Filter frequency response

$X(w)$ = Input in the frequency domain

In the equation that you wrote the two "*" symbols mean different things.  In the time domain it is convolution, in the frequency domain it is multiplication.  The equation is just saying that convolution in the time domain (which is how you do time domain filtering) is equivalent to multiplication in the frequency domain.