I’ve got a portable new short-wave radio with a standard telescoping antenna, the kind that have been on radios from time immemorial. Why does extending the antenna improve my radio reception?
I’m not a ham, but I play one on TV . . .
Two reasons come to mind:
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Height of the antenna. Height really improves the distance of a radio. Usually, radios can take the advantage of either line-of-sight or a troposphere/earth bounce angle and can benefit from a higher antenna.
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Wavelength. The longer the wavelength down your transmission line, the more wattage is output from your antenna. This is why a lot of radio operators check their standing wave ratio and make sure it’s at 1.00 as best as they can make it.
I’m a EE by training, and IIRC, #2 is subject to question. But, call it an informed educated guess.
Tripler
Like I said, I play one on TV. 
Radio waves are electromagnetic waves made up of oscillating electric and magnetic fields. An electric field exerts force on charged particles, and the particle will move back and forth if it’s not fixed. Electrons in a metal rod are not fixed, so a radio wave causes electrons to move back and forth along the metal. Movement of electrons is an electrical current, so that’s an electrical signal right there. You just need to amplify it, pick out the right frequency and extract the signal from it. If you make the wire longer, you are exposing electrons to a larger area of the incoming wave so the more current you get. Longer is not always better though - if it’s longer than the wavelength of the radio wave, the extra length won’t do any good. The electrons will just be dancing back and forth near the end of the antenna and never reach the amplifier. That’s why you use tiny antennals for UHF television, and longer antennas for shortwave radio.
An analogy would be to use a float to measure ocean waves. Imagine a styrofoam float connected with lever arms to a measuring device. The waves cause the float to go up and down. The mechanism has some friction, so you want to use a large float which will push the lever arm harder. But if you make the float too large, you won’t be able to measure small ripples (i.e. short wavelength waves).
(That’s a gross over-simplification but I don’t think that’s far off conceptually.)
To reinforce what scr4 said, antennas work best when they are resonant at the frequency of interest. Failing that, and for shortwave signals the antennas are tens of meters in length, a longer antenna intercepts more of the wavefront and supplies a stronger signal to the radios circuitry.
Also what scr4 said: a longer antenna intercepts a larger area of the incoming wave. Ideally the radio waves hit the side of the antenna. Although a telescoping antenna is thin, electrically it behaves like a very wide absorber plate (like a sail catching the wind, or like a solar cell.) If your antenna is 2ft long, it actually behaves like a 2x2 plate.
A thin antenna acts “wide” because the radio waves cause a current in the antenna, but the current in the antenna creates an “answering” wave, and this second wave cancels out the incoming wave. The “cancelled” energy ends up inside the radio. And, since the region of cancellation around the antenna is fairly broad, the thin little antenna can grab a huge bite out of any waves that hit it. The longer the antenna, the bigger the area of the radio wave being absorbed.
This only works for antennas up to 1/2 wavelength in length. Making your whip antenna any longer than half-wave won’t grab any more energy.