Yep, they're much more efficient than good old filament light bulbs and draw less current. Alternatively you can buy really bright ones designed to use more power!
They are polarity sensitive so for DC you have to get the wires connected correctly to positive and negative as has been mentioned. For AC they're only lit for half the cycle (sometimes noticeable on video cameras etc.)
A typical LED only needs a couple of volts in order to light up (it varies by colour, with some needing over 3V). To operate with higher voltages a resistor is needed to drop the extra volts and also to limit the current flow.
If you're not yet familiar with them and how to calculate the required resistor, then you bought sensibly by choosing pre-wired LEDs with a suitable resistor pre-fitted for the expected voltage they'll be used at.
I have frequently googled a programme to calculate the resistor needed - can't remember the link, but just google 'calculate resistor for LED or some such and you'll find it.
One of the biggest advantages of LEDs (apart from their minimal current draw) is with battery powered locos, because, as others have said, LEDs are an electrical one way street, so if you get your wires the right way around you have instant, simple, directional lighting - even I managed to work it out on the first battery loco that I ever built, so it's got to be quite easy
Oh yeah, you cant get flashing ones as well, then you can really have fun
This has two LED headlights, and two flashing red LEDs on the roof