Electrochemical energy is one of the many interchangeable forms of potential energy through which energy may be conserved.  It appears in electroanalytical chemistry and has industrial applications such as batteries and fuel cells. In biology, electrochemical gradients allow cells to control the direction ions move across membranes. In mitochondria and chloroplasts, proton gradients generate a chemiosmotic potential used to synthesize ATP, and the sodium-potassium gradient helps neural synapses quickly transmit information.
An electrochemical gradient has two components: a differential concentration of electric charge across a membrane and a differential concentration of chemical species across that same membrane.  In the former effect, the concentrated charge attracts charges of the opposite sign; in the latter, the concentrated species tends to diffuse across the membrane to an equalize concentrations.  The combination of these two phenomena determines the thermodynamically-preferred direction for an ion's movement across the membrane.
The combined effect can be quantified as a gradient in the thermodynamic electrochemical potential: with   Sometimes, the term "electrochemical potential" is abused to describe the electric potential generated by an ionic concentration gradient; that is, . 
An electrochemical gradient is analogous to the water pressure across a hydroelectric dam. Routes unblocked by the membrane (e.g. membrane transport protein or electrodes) correspond to turbines that convert the water's potential energy to other forms of physical or chemical energy, and the ions that pass through the membrane correspond to water traveling into the lower river. Conversely, energy can be used to pump water up into the lake above the dam, and chemical energy can be used to create electrochemical gradients.