What makes an Antenna special? The most important property of an antenna, beyond its conductivity(?) seems to be it's length (or more generally, its shape).  But the antenna device is connected to the receiver by an arbitrarily-long connector.  What is the fundamental difference between an antenna and the connector?  Why doesn't the connector's length, straying from some 1/2, 1/4 length of the targeted band, interfere with the reception?
 A: Please allow me to quote from one of my old text books - Transmission Principles for Technicians, D C Green:

Whenever a current flows in a conductor, the conductor is surrounded by a magnetic field, the direction of which is determined by the direction of current flow.  If the current changes, the magnetic field will change also.  Now, a varying magnetic field always produces an electric field that exists only while the magnetic field continues to change.  When the magnetic field is constant the electric field disappears.  The direction of the electric field depends on whether the magnetic field is growing or collapsing and can be determined by the application of Lenz's law.  Similarly, a changing electric field always produces a magnetic field; this means that a conductor carrying an alternating current is surrounded by continually changing magnetic and electric fields that are completely dependent on one another.
If a sinusoidal current is flowing in a conductor the electric and magnetic fields around the conductor will also attempt to vary sinusoidally.  When the current reverses direction the magnetic fields must first collapse into the conductor and then build up in the opposite direction.  A finite time is required for a magnetic field and its associated electric field to collapse, however, and at frequencies above about 15KHz not all the energy contained in the field has returned to the conductor before the current has started to increase in the opposite direction and create new electric and magnetic fields.  The energy left outside the conductor cannot then return to it and instead is propagated away from the conductor at the speed of light.

So that deals with how radio waves are produced.  Now, what makes an aerial special?
Well, that is all to do with the wavelength ($\lambda$) of the signal.  When an alternating current reaches the end of a transmission line it "bounces" back again (echoes) back down the line.  This is a big problem when it's not wanted, as the reflected signal can interfere with the rest of the signal causing extra noise and attenuation of the signal.  This is why proper termination of transmission lines is essential, to absorb these reflections.
However, the same phenomenon can be made use of to boost the signal level.  If you measure the transmission line (in this case the aerial) to be precisely a hole division fraction of the wavelength of the signal (most commonly $\frac{1}{4}$ but $\frac{1}{2}$ or $\frac{1}{8}$ are used) it is possible to get the reflections to add to the signal, thus boosting it.
The same goes for the received signal in a reception aerial.  As the incoming signal inducts a voltage in the aerial reflections will be produced from the open end of the aerial.  These reflections are added to the signal to boost the signal level and quality.
So the aerial, due to its precisely measured length, can be "tuned" to a specific frequency.
Also, there are more complex designs of aerials than just a length of wire.  Such designs as the Yagi Array which adds a directional component to the radiation of the signal.  The aerial includes a "reflector" which bounces the signal that goes behind the aerial back in a forward direction.  By careful position and measuring of the reflector it is possible again to get the waves of the signal to line up and thus increase in power, just like the reflections in the single-wire aerial.
A: The pair of wires which leads signals to/from the antenna uses a simple trick: In order not to radiate they are configured so to carry opposite currents. The radiation from one wire cancels the radiation from the other wire.
This also helps in the other way: The radiation picked up by one wire cancels the radiation picked up by the other wire.
The simplest version is the "twisted pair". Two parallel wires with anti parallel currents still have some remaining radiation mainly in the plane which intersects the wires. This can be improved by twisting the wires around each other to better cancel radiation over 360 degrees. 
Better, but more expensive, is the coax (co-axial) cable in which the outer wire is a cylinder surrounding the inner wire. The radiation from the anti-parallel currents is compensated equally well in all directions.
A: If you apply an alternating electric current on a piece of wire,  it will radiate. For example we live in a 50 Herz background in our houses because of the wires bringing in the electricity.
A receiving antenna is oriented and has the size necessary to receive signals for  the TV or radio. In order to shield the wire connecting the television to the antenna, so there is no interference of unwanted frequencies, one uses special wires called coaxial. They have a core wire which carries the signal and are covered outside with wire mesh or aluminium foil in order to shield from any ambient signals the small wanted signal. 
If one uses a transmitting antenna the same logic holds. The wires carrying the signal to the aerial are coaxial.
