Age is a measure of how old something is. If you have just celebrated your tenth birthday, you are ten years of age, or ten years old.
Distance describes how far apart two points are, or describes something that is a long way away, for example "you can see the hills in the distance". The men in the picture are making a fence with all the posts the same distance apart.
Height is the vertical measurement of a person or object from the ground to the top of the head or the highest point of an object.
Size is a measure of how big something is. You can measure size in defined units like inches, or you can use descriptive words like big, small, tiny or huge.
Speed is the measure of how fast something is moving. The car in the picture is moving very fast, while a snail moves slowly.