Look at the middle letter of convex and you can see it is the start of a convex surface.
A CONVEX SURFACE CURVES OUTWARD
Convex surfaces curve outward and it tells you in the name.
A convex lens looks like the following:
But because convex lenses are defined as being thinner at the edges and thicker in the middle, a convex lens only needs to have one surface that curves outwards: the other can be flat.
A convex lens is a lens that possesses at least one surface that curves outwards.
NOTE: The above diagram shows convex lenses called plano convex lenses. An easy way to recall this is to remember that one surface is a plane (flat) and the other side looks like half an "O".
Plane "O" = Plano convex
Convex lenses are sometimes denoted by a symbol:
This is drawn as a vertical line with outward facing arrows to indicate the shape of the lens is thicker in the middle.