The storage method in SD cards and other modern large flash semiconductor based storage is mostly a technology called NAND flash.
http://en.wikipedia.org/wiki/Flash_memory

The storage node itself is a transistor structure called Floating Gate.
http://en.wikipedia.org/wiki/Floating_Gate_MOSFET

The value stored in the Floating Gate is either an "1" when empty, or "0" when charged with electrons. The Floating Gate itself is insulated with oxide layers so the electrons trapped will not escape from the FG.

When the device is empty, they are usually consider as field of "1"s and the writing process is placing a strong electric field on the Control Gate. This causes either Hot Electron or Fowler-Nordheim tunneling to occur and electron crosses the insulating oxide layer into the FG. Once the electrons are in the FG, they are trapped essentially for eternity. These are considered as "0" values.
http://en.wikipedia.org/wiki/Field_electron_emission

But, manufacturing process is not perfect so the oxide layer, thickness measured in Angstroms, can have in perfections and cause the electrons to leak out of the FG. Flash devices are then designed with error detection and correction features. When there are so many errors that the error detection and correction cannot handle it, that is when a card reports file errors and rendered useless.

Usually placing "0"s into the FGs are relatively fast but erase back to all "1"s are slow. This reflects in different performance level in different cards due to improving designs and manufacturing processes.

Theoretically electric fields can affect Floating Gates but the field used are so strong and precise that essentially it is safe from common electric fields.