Core Body Strength
Core body strength is the ability to use muscles other than your arms to hold you in different positions. Some of the core muscles that are used for climbing are upper and lower abdominals, lower back, hamstrings, and calfs. Generally think of the core muscles as the ones that allow you to keep you feet on a roof, or to pull yourself onto a rock on without bending your arms. Body tension or the lack thereof is a result of core body strength and knowing how to use it.
Core Body Strength Drills:
Dead hang from good holds and lift your legs straight in front of you, bending at the waist. Lift your legs until your body forms a 90 degree bend and lower slowly. Try not to swing or kick your legs up. If you cannot stabilize yourself have a partner stop your swinging. If you cannot do a leg lift with your legs straight then bend your legs at the knees to 90 degrees. Keep your knees bent at 90 degrees for the whole range of motion both up and down. Do this until failure or repeat as many times as possible in one minute (if you cannot do this for a minute straight). Complete three sets with a one minute rest between sets.
A good climbing variation on this is to find a roof and grab a large hold with both hands. Lift your feet off the ground and lift one foot at a time and place it on a foothold. To make this harder put the feet farther away and practice accuracy with your feet. Modify the holds from underclings, sidepulls, and straight downpulling so simulate different climbing movements. The key is to place your feet directly onto a hold, tighten up (let your feet take some weight) and then release.
Lie on your back and extend your arms straight above your head. Straighten your legs and then bend at the waist about 20 degrees (form a banana). Slowly rock back and forth keeping your lower back on the ground and pointing with your toes and fingers.
Try to move slowly and don't let your head or feet touch the ground. Do this until failure or repeat as much as possible for one minute. Try to do this in sets of three with a one minute rest in between.
Lie on your stomach and extend your arms straight in front of you. Move your arms and legs up and down in a small range of motion trying to keep your quads off the ground. Try to keep your legs straight, but your arms may be slightly bent.
Start on your hands and knees. Raise opposite arm and leg (left arm, right leg) at the same time to a horizontal position. From there lift the arm and leg in a reverse crunch and lower back to horizontal (one rep). Without letting you hands or feet touch the ground pull up again and repeat until failure. Do this with the other leg/arm for a minimum of one minute each side. Try to do three sets of this exercise for each side.