Forward-bias is when the anode (the pointy part of the symbol) is positive and the cathode (the bar) is negative. Reverse-bias is when the anode is negative and the cathode is positive. A lot of current flows when the diode is forward-biased, provided that the voltage is higher than 0.6V or so for a silicon diode or 0.3V or so for a germanium device. A very small amount of current flows if a diode is reverse-biased.
If you have a DVM and some diodes, you can check it for yourself. Diode cathode leads are usually identified with a band, so if you switch the DVM to a low resistance setting, and connect the leads across the diode in both directions, you should see a low resistance in one direction and a high resistance in the other direction, provided that the DVM is supplying a high enough voltage. Some DVMs have a special diode test setting that is easier to use.
LEDs usually have a flat against the cathode lead.