Repeaters are automatic ham stations, with their own call sign. They are typically located on hills where they have a large area of coverage.
They are automatic in the sense that they do not normally have a human operator at the controls. They are set up to listen on their assigned frequency, and when they hear a transmission on their frequency (that also contains the correct code - see below), they "repeat" the transmission (on a different frequency - see below).
Given that someone sending a transmission to a repeater might be located at a lower elevation and might not have a wide area of signal coverage, still if they can "hit" the repeater, the repeater will re-transmit their message to the wider area of coverage that the repeater transmitter has because of its higher elevation.
Repeaters therefore act as relays, passing along the communications sent to them.
Offset Frequency:
Repeaters receive on one frequency, and transmit on a different frequency.
The "posted" frequency for a repeater is the "transmit" frequency from the repeater. This is the frequency you set your radio on when you are listening to what the repeater is transmitting.
The difference between the transmit and receive frequencies for a repeater is called the "offset." offset = freceive - ftransmit
So eg. for Stacker 70cm in the table above, the freq listed in the table is the repeater's transmit frequency, 444.700 MHz, and your radio should be set to receive on this frequency.
Your radio should be set to transmit on the repeater's receive freq, which is
freceive = offset + ftransmit
freceive = 5 MHz + 444.700 = 449.700 MHz
Typical offsets:
"Typical" means this is the way most repeaters are set up. But it's not a rule/requirement, and repeater operators are free to set up whatever offsets they want.
But there are typical/conventional values:
70cm band: +/- 5.0 MHz
1.25m band: +/1 1.6 MHz
2m band: +/- 600 KHz (0.6 MHz)
10m band: 100 KHz (0.1 MHz)
There are also conventions for which portion of a given band will have a "+" offset, and which part will have a "-" offset.
Don't have this information at the moment ...
PL or CTCSS tones
"PL" = "Private Line"
"CTCSS" = Continuous Tone-Coded Squelch System
This is a method of ensuring the repeater does not respond to random transmissions on its frequency, but only to transmissions intended for it.
If you want to use a repeater, you must program your radio to output a CTCSS tone that the specific repeater expects. These tones are typically low-frequency (virtually inaudible) in a range of 67 - 254 Hz.
The repeater will not respond (ie. will not repeat) any signals that it receives that do not have its expected PL tone.