Power
Adds 25% damage to all RAW (physical) damage you do in Sword mode.
Element
Adds 25% damage to all Elemental damage you do in Sword mode.
Dragon
Adds Dragon element to all your attacks in Sword mode, which is the type of damage Dragons are the weakest to (i.e. Rathian, Rathalos). The exact amount depends on the weapon.
Paralysis
Attacks in sword mode will do paralysis. The exact amount depends on the weapon.
After doing enough Paralysis damage to a monster they'll be stunned for a short while. The amount of paralysis damage you need to inflict, and the duration of the monsters stun, varies based on the monster. Take note that after you stun a monster, it becomes harder to stun it again. Additionally, paralysis damage is "removed" from a monster over time, so you need to keep attacking in order to paralyze the monster.
Poison
Attacks in sword mode will do poison damage. The exact amount depends on the weapon.
After you inflict enough poison damage on a monster they will be poisoned for a predetermined duration, and will take damage over time. Like paralysis, the duration and amount of poison damage required to inflict it depends on the monster. It will also be removed over time, and becomes harder to apply on the monster with each successful application of it.
Exhaust
Attacks in Sword Mode will do Exhaust damage. The exact amount depends on the weapon.
Exhaust damage inflicted on the monsters head will do KO damage. After a certain amount of KO damage is dealt the monster will be knocked over for a short period. Do note that like other status ailments the KO damage inflicted on the monster will decrease over time, so it's important to keep attacking the head if you wish to knock the monster out.
Exhaust Damage inflicted anywhere but the head will do stamina damage, which drains the monsters stamina. When using a Switch Axe that does exhaust damage you'll notice monsters will begin drooling a lot faster than normal, resulting in them being less effective in battle.
Best Answer
The location of that meter is reserved weapons with a unique functionality which require an additional bar. It's functionality varies from weapon to weapon, and doesn't even exist for some weapons. Other weapons will have something else in it's place which isn't a meter at all.
The weapons which make use of that spot are:
Dual Sword: Demon Gauge. To be honest, I'm not that familiar with the Dual Swords, so I'd suggest looking into this video tutorial for more information. The basic idea is that Dual Swords can enter something called Demonization mode, which gives you additional combos and improves you attacks. When you hit monsters in demon mode the meter fills up, and so long as the meter isn't empty you'll do extra damage and attack faster when not in demon mode.
Long Swords: Spirit Gauge. Once again, I'm not that familiar with the Long Sword, so I'll refer you to here for more information. Attacks with a Long Sword fill up the Spirit Gauge. Once the Spirit Gauge is full, Spirit Attacks (made with the R button) no longer cost Spirit. A Spirit Combo performed while the Spirit Gauge is full will have a finishing attack called the Spirit Roundslash. Your hunter will automatically sheathe his/her weapon after performing a Roundslash and receive a minor damage boost. Landing the Spirit Roundslash will also increase the grade of the Spirit Gauge (white -> yellow -> red). Higher grades of the Spirit Gauge will provide higher damage boosts while degrading quicker.
Bowguns / Gunlance: These weapons require ammunition, and they use this spot to displays how much ammo is remaining in the weapons clip.
Switch Axe: Phial meter. The Switch Axe has two modes, Axe and Sword, and every Switch Axe has a phial. Axe mode generates phial energy, and Sword mode consumes it. The functionality of the phial varies from Axe to axe, but are only active when in sword mode. For example, a Power Phial will boost the Raw (physical) damage you do. The phial meter displays how much phial energy you have left.
Hunting Horn: Note meter. The Hunting Horn produces a musical note with every attack, which are displayed in the note meter. Some sequences of notes allow the Hunting Horn to play a song by pressing the R button, which gives the the user and nearby allies a temporary buff. Their are a variety of buffs, including healing, attack boosts, and giving users infinite stamina.