Deriving phase of a pulsating star from list of Julian date values of observing brightness
INT refers to the floor function. So $\mathrm{INT}(x)$ is the largest integer not exceeding $x$. 

In this case, the function is used to get the fractional part of $\frac{\mathrm{HJD}-T_0}{P}$, i.e. the part after the decimal point. So if for example $\frac{\mathrm{HJD}-T_0}{P}=3.4$, then $\frac{\mathrm{HJD}-T_0}{P}-\mathrm{INT}\left(\frac{\mathrm{HJD}-T_0}{P}\right)=0.4$.