A transverse wave oscillates perpendicular to the direction of its propagation. In other words, the paths of oscillation of the particles or elements of the medium are at right angles, or perpendicular, to the direction in which the wave is traveling.
To understand what is meant by "right angles," it refers to a 90-degree angle. When two lines intersect, and the angles formed at the intersection point are each 90 degrees, they are said to be at right angles to each other. This means the lines are perpendicular to each other.
In the case of a transverse wave, if you imagine the wave propagating horizontally from left to right, the particles of the medium (such as molecules or segments of a rope) move up and down or side to side perpendicular to the direction of wave travel. The motion of these particles is at right angles to the wave's direction of propagation.