The word "Elevation" is used in several different contexts quite frequently in hiking and back-packing and can cause confusion for some people.
The first use refers to the actual height of a hill or mountain. For example Half Dome stands at 8,839 feet. This number refers to how high the peak of Half dome is. The second use refers to the general elevation you are hiking at. For example if you were hiking from Cathedral Lakes to Sunrise Likes in Yosemite, you might say "I did a two day trip at about 10,000 feet." In this instance you are referring to a generalized average elevation you were hiking at even though you may be lower or higher and moving up and down throughout the hike.
The third use, and most commonly confused use refers to "Elevation Gain" (EG). This refers to the total feet climbed throughout a hike and usually is a completely different number to the elevation of the peak.
If we use the basic drawing above, lets work off some assumptions to illustrate this example.
You are starting at sea level (0 ft)
The hill has an elevation of 1,300 ft
But what will be your elevation gain to reach the peak?
The first section is 0 ft, climbing to 500 ft (Total EG 500 ft)
You then descend 200 ft (to 300 ft) and climb to 1,000 ft (Total EG 700 ft)
You then descend 200 ft (to 800 ft) and climb to 1,300 ft (Total EG 500 ft)
So in this instance, even though the hill stands at an elevation of 1,300 feet, it requires a hike of 1,700 feet to actually reach the summit - 1,700 is the Elevation Gain.