I’m not much of a physicist, but in direct current the charge only flow in one direction, whereas in alternating current, the direction the charge travels in changes (alternates) periodically.
Alternating current is more efficient when the charge needs to be carried a long distance to get to the thing it is trying to power and direct current is used when the charge only needs to travel a short distance.
Sophie has it spot on, with Direct Current (DC) the electrons all flow in one direction from positive to negative supply – most things that run off a battery will be DC. With Alternating Current (AC) the electrons flow back and forth (in the UK this occurs at a frequency of 50Hz or just under once a second). This makes it more efficient to transmit the power over long distances which is why the sockets in your house operate on 240Volts 50Hz AC power.
The other big difference is in the components that you would use on each type of circuit. Motors are a good example – a DC motor from your remote controlled toy at home will not work in an AC circuit without some significant circuitry to protect it and likewise the motor from your hoover at home would not run off a battery.