The Mount and the Guard
In the mount (a), the person on top has their legs astride the chest of the person on the bottom. This is a very advantageous position for the person on the top. In fact, for the person on the bottom, this is the single worst position to be in in a fight.
The reason why this is so bad for the person on the bottom is mainly due to punching. Due to the relative position of the shoulders and faces, the person on top can punch the face of the person on the bottom (b), but the person on the bottom cannot punch the face of the person on the top.
Furthermore, the person on top has gravity on their side to aid their punch (b) and can fully cock their arm. The person on the bottom cannot fully cock their arm as it is blocked by the ground (c).
When the person on the bottom is able to use their legs to control the hips of the person on the top, then they have the top person in their guard.
In the near guard (d) \& (e) the person on the bottom has their legs wrapped around the hips of the top person. The opponent is clinched close, so that they do not have the distance to punch. The bottom person uses their legs to control the hips of the top person.
In the far guard (f) \& (g) the person on top is kept away with the knees. In this position, the top person is too far away to effectively punch at the bottom person's face.
The Triangle Choke
This is the choke that Royce Gracie finished off Dan Severn with in UFC IV. Renzo Gracie seems particularly fond of this one as well.
A triangle choke is a useful choke to use from the guard. It is a defense against someone trying to pass the guard (a).
As they try to pass, they put one leg on their shoulder (b). (In this picture, your right leg.) Unlock your legs and pull their right arm down and across your body (b) \& (c). At the same time you want to get the crook of your left knee over your right ankle (c). This is often hard to do. It helps to get your right shin horizontal and to slide your hips to your right. You may have to use your hands to lock your left leg over your right (b) \& (c).
Once you get the left leg folded over (d) \& (e) this is an incredibly powerful choke. Fold your left leg down while pulling their right arm towards your right shoulder (c) \& (e). Stretch your hips back (e) while holding their arm.
Extra pressure can be applied by releasing their right arm and grabbing the back of their head (d) \& (f). Pull the head down into the V formed by your thighs while stretching the hips out (e).
This is very much like a Kata Gatame, put on with the legs.
Their defense involves early on reaching with their left hand acroos your neck and securing the lapel (g). From here they drive forward and down to put a choke on with their forearm. It becomes a question of who does it best -- soonest.
Finishing Move: Going from mount to arm bar.