Using LED lamps on household AC power
A single LED is a low-voltage solid state device and cannot be directly operated on household AC current without some circuit to control current flow through the lamp. A series resistor could be used to limit current, but this is inefficient since most of the applied voltage would be wasted on the resistor. A single series string would minimize dropper losses, but one LED failure would extinguish the whole string. Paralleled strings increase reliability. In practice usually 3 strings or more are used.
Lamp sizes and bases
LED lamps intended to be interchangeable with incandescent lamps are made in standard light bulb shapes, such as an Edison screw base, an MR16 shape with a bi-pin base, or a GU5.3 (Bipin cap) or GU10 (bayonet socket). LED lamps are made in low voltage (typically 12 V halogen-like) varieties and replacements for regular AC (e.g. 120 or 240 VAC) lighting. Currently the latter are less widely available but this is changing rapidly.