A quadrilateral is a shape with four edges and four vertices. For example, a square is a quadrilateral, as is a trapezium.
A convex quadrilateral is one where any line that can be drawn between any two points lying in the quadrilateral is fully contained in the quadrilateral.
One can easily see how any conceivable line drawn in a square, rectangle, or trapezium is contained in that shape, implying that all of these are convex quadrilaterals.
In order to see a case where a quadrilateral is not convex, consider the shape below. The red line drawn is such that it starts end ends in the shape, but a portion of it lies outside the shape.
The idea of convexity exists similarly for any other polygon. In a very interesting fashion, it is also similarly meaningful in a non-geometric way.