Is this worth playing online?

[Namillus]

You refer to Synthesis, better known as Item Crafting. This is not required to play the game, but does allow you to create cheaper weapons, albeit with a chance of failing and receiving a nigh-useless item instead. Another advantage of Synthesis for Hunters and other types dependant upon melee weapons is the ability to create weapons with the element of your choice.

Essentially, while you explore missions, items resembling pyramids with a symbol at the point of the spire drop, as opposed to the saber-shapes of Weapons, the diamonds of Tools and Consumables, and the shield-shapes of Armour and Units. These are stored in the fifth page of your items menu. These items range from natural materials (Berries, Woods, Silica, Acids, and Biomaterials) to artificial (Metals, Ores, Photons, Gems, and Chips).

You can buy Synthesis Boards from Synthesis Shops for practically any item at the moment, but sometimes it can be more productive to buy the completed item from the primary manufacturer's store - for example, there is no real need to synthesise casting weapons or guns, since you cannot give these elements during synthesis, only through Photon Art linking, hence, rather than risk failing and spending additional money on more materials, you can obtain a completed version. Note, though, that synthesis boards are about half the price of the actual item, and in addition have multiple uses.

It is not required to synth to progress in the game, nor is it required to feed your Partner Machine. However, feeding the Machine gives you a better shot at synths, and eventually gives you the benefit of a decent battle partner.

Basically, you can buy anything you really need 'vanilla' from the maufacturers. But if you want your own personal touch on a weapon (A Lightning Calibur, for instance), synthing's the way to go.