Interaction terms can be introduced to your model to account for different effects when two independent variables combine in some interesting way.
They are commonly used when categorical factors are present, e.g. to allow different rates of response of $Y$ (income) to a second factor $X_{2}$ (years of education) according to the categorical $X_{1}$ (gender, 0=male, 1= female). If we simply regress $Y = \beta_{0} + \beta_{1}X_{1} + \beta_{2}X_{2}$, the model only accounts for females earning a fixed amount more or less than males, with a separate term accounting for educational difference regardless of gender.
If we add a third interaction variable $X_{1}X_{2}$, so $Y = \beta_{0} + \beta_{1}X_{1} + \beta_{2}X_{2} + \beta_{3}(X_{1}X_{2})$, this third factor will be zero for males, but non-zero for females, thus representing the specific variable female years of education, and allowing the model to separately account for the effects this on income ($\beta_{2}$ becomes the gradient for rate of change of male income, and $\beta_{3}$ is an adjustment to the slope of income change for females).
This is an interaction, but it is not collinear, because it does not respond the same way as years of education across the full data set (it is zero for all points that are male). Thus, interaction is not the same as collinearity, and interaction can in fact be a useful element of a regression model.
More generally, the multiplication of two variables (both non-constant) is by definition non-linear, so while an interaction term created in this way may be related to the two component variables, it is not related linearly so collinearity is impossible.