What's the difference between dimmable and non-dimmable LED lamps?
Most LED bulbs on the market are in fact dimmable, IF you use a CFL/LED dimmer.

Your "standard" dial or track dimmer is either just a big potentiometer or Rheostat that reduces voltage through resistance, or a slightly more efficient design called a TRIAC dimmer, which uses a specialized transistor design to attenuate the line voltage by turning the line on and off based on where the AC is in its "rhythm" or "phase".

These dimmers work just fine for incandescents, but cause problems for CFLs and LEDs. A CFL needs a big power spike to get started, but then as long as it gets enough power (about 13w for a 60W-equivalent) it'll happily produce full light. LEDs are similar, but instead of needing a power spike to get started, they need DC current, produced by first "stepping down" the AC current and then running it through a diode and capacitors to restrict the flow to one-way. This is the same technology used in AC adapter "wall warts". The problem here is that the capacitors, which charge when the power is flowing the "right way" through the diode and discharge when the power is blocked by it, hold plenty of charge to keep the LEDs going when the power is cut off for slightly longer periods, such as by a TRIAC dimmer. In fact, many of these AC/DC converters have some sort of rectifier, like a TRIAC or SRC, built in to attenuate the power (the transformer will exchange voltage for amperage, or vice-versa, so you have to further cut down the current from line level), so the capacitor bank is DESIGNED to handle this type of current.

CFL/LED dimmers reduce power in a different way; they turn the power on, then off for set periods of time (i.e. "on for 10ms, off for 5ms"; as opposed to TRIAC dimmers' "on as long as the phase isn't x degrees or closer to peak power"). This still reduces RMS power over the entire waveform, but it does so in a way that CFLs and LEDs respond to more readily.

You still need special bulbs as well as special dimmers to dim energy-efficient bulbs. CFLs need a ballast that can charge and discharge very quickly (the technology found in "instant-on" CFLs that can "ignite" within just a few milliseconds) in order to turn on and off fast enough to make a difference. LEDs, for their part, react more naturally to the longer "off" periods of a CFL dimmer than a TRAIC, and so most LEDs can be dimmed to some degree, but you don't get a very smooth dimming across the full range. Many newer ones instead use integrated circuitry (yes, there are computers in your freakin' light bulbs now) that will "sense" the on-off pattern and translate it to a more rapid succession of "clock pulses" to "blink" the LEDs. This bypasses any problems with the capacitors keeping the LEDs going and results in more gradual dimming.

Now, there are brand-new LED bulbs that are dimmable with TRIAC dimmers; the IC controller in the bulb is designed not only to correctly distinguish CFL dimmer "on-off" patterns, but TRIAC "on-off" patterns as well, so it can translate both of them into the rapid pulsing used to control LED light levels.