Tangency

Two smooth curves have tangency at a shared point when their tangent lines agree. A tangent to a circle is perpendicular to its radius at the contact point: at $(r,0)$ on $x^2+y^2=r^2$ the tangent is $x=r$. For smooth surfaces the analogous condition uses tangent planes. Tangency is local and does not preclude crossing: $y=0$ and $y=x^3$ have the same tangent line at zero but pass through one another there.