It's not really called "Limit Break" here. The term used in this game is "Weapon Skill," (abbreviated by WS) a weapon-based skill you used to deal extra damage when you gain 100% or more TP (technical/tactical point or something, which you can gain by hitting a monster). In order to create a skillchain, or renkei (its Japanese name; skillchain is abbreviated by SC), Melee A first use his weapon skill, follow by Melee B using another weapon skill a brief while (about 2 to 3 seconds) after the first. If it can connect, it will create a skillchain effect which can deal extra damage to the monster.
There are three levels of skillchain and each skillchain can be of a certain element. Level 1 consists of Liquefaction (fire), Induration (ice), Detonation (wind), Scission (earth), Impaction (thunder), Reverberation (water), Compression (dark) and Transfixion (light).
Level 2 consists of Fragmentation (thunder and wind), Fusion (fire and light), Gravitation (dark and earth) and Distortion (water and ice).
Level 3 consists of Light (light, fire, wind and thunder) and Dark (ice, water, dark, and earth).
The more elements there are in a skillchain, the more damage a skillchain can do. So that would make level 3 the strongest, follow by level 2, then level 1. You should also factor in the elemental weakness of the monster your party is fighting in order to determine the best skillchain to use to deal more damage. Besides factoring in the monster's elemental weakness, you also need to take notice of the melee's weapon skill. The damage of a skillchain is mostly determined by the damage of the second weapon skill (the ender). So while if weapon skill that does low damage ends the skillchain, the skillchain effect will not be able to deal more damage. Whereas a weapon skill that do very strong damage ends the skillchain, the skillchain effect will be able to do more damage, provided the monster did not resist it.
So all in all, when relying on skillchain to deal damage (which every party should do in my opinion) pre-65/65, it is best that you find the weapon skills that can create a level 2 skillchain effect while dealing a lot of damage. Just a tip.
Anyway, continuing on. Since you are a BLM, you would need to participate in a skillchain as the magic burster (magic burst; abbreviated by MB). What a magic burst do is that when a mage casts an offensive spell of an element that is the same as the skillchain's element(s), its potential can be increased. Besides doing this for the stylish factor, it can also increase the power of a BLM's nuke.
For example, Melee A uses a weapon skill and Melee B follows up with another weapon skill to create a Fragmentation skillchain. Right after the combined weapon skills created Fragmentation skillchain, if a BLM casts elemental spells of thunder or wind, a magic burst effect will be achieved. Say if a BLM casts Thunder and it normally deal about 100 damage, achieving the magic burst will cause the Thunder do more than 100 damage. This is a really important aspect of the battle system in this game as skillchains and magic bursts deal so many extra damages that monsters die faster and experience points will be gained faster.
As a BLM, that is what you need to focus on. Learn about the weaknesses of the monsters you are fighting when you level and know what skillchains are best used against them. Having those knowledge will definitely help you become a better BLM and it will make your parties much better than the average Joes.
I know my explanation may be a bit difficult to understand. So here is a link if you want to read an alternative explanation of skillchain and magic burst. I got this link from the official PlayOnline site. It is an article in the Vana'diel Tribune that talks a lot about the elements of skillchain and magic burst.
http://www.playonline.com/ff11us/vt/extra/index.html
By the way, here is a very useful skillchain chart that you should get to know better. It helps a lot.
http://www.adennak.com/renkei.html
If you have any more questions, feel free to ask. I'll be sure help you if I can. Happy learning. ^^