[RyanGuyardo (OP)]

I'm planning to lengthen my earphone wire simply because it is too short.

I notice that the inner wire is insulated or has a coting.
What's that? and What's that for by the way?

[RD]

Earphone cable is shielded to prevent interference, (like mains hum), being picked up. 

Headphone extention cables are available for about £5 ... http://www.maplin.co.uk/Module.aspx?ModuleNo=11425&C=SO&U=strat15

[LeeE]

If the device you're using the earphones with is also an VHF i.e. FM radio receiver, the earphone leads may also be acting as the aerial for the device.  If so, changing the lead length is likely to adversely affect radio reception (mind you, they're usually pretty crappy anyway as they can't be laid out properly and be worn at the same time).

[lyner]

The coating on many of the wires for this sort of application is insulating but the insulation can be melted by a soldering iron and makes it convenient to assemble because you don't need to strip the wire to solder it.
Changing the length won't make much difference to the RF reception. Your body and other nearby objects will have just as big an effect, if not more.

[Soul Surfer]

Earphone cable is also often very fine wire mixed with strong fibres to make it very flexible and strong because they often get pulled about.  You may have tosort these out or they could make it dofficult to solder to.  You can get extension leads with sockets on one end and plugs on the other if it is just the combined lead you wish to extend and there is no logical reason to extend the earpiece leads unless you have a remarkably big head!

[lyner]

I soldered one the other day and it tinned a treat.

[techmind]

I'm planning to lengthen my earphone wire simply because it is too short.

I notice that the inner wire is insulated or has a coting.
What's that? and What's that for by the way?

You are likely to find that each half of the normal "figure 8" lead contains two conductors, either coaxially or insulated with a thin coating and gently twisted.

Each conductor will comprise many fine copper wires (more, finer wires = more flexible) and possibly some sort of cotton thread (for mechanical strength).

These days it's usually best (and cheapest) just to buy a ready-made extension lead, complete with plug and socket.