There are two different time systems available on IGS-Pandanet: Pandanet style and Byoyomi style.
This time system is also known as Canadian time. Each player starts with an initial main time. Once the initial time has run out, a player gets a fixed time for a certain number of stones to play, usually 25 stones. When those 25 stones have been played, the clock will be reset to the original value.
For example "1/10" (often seen in game annoucements in Shouts) means 1 minute initial time plus 10 minutes for 25 stones. First each player gets 1 minute main time, afterwards the clock shows 10:00 (25) meaning there are 10 minutes available to play 25 moves. Now it will go down like 09:42 (24), 09:28 (23) etc. with each move. Once the 25th move has been played, the clock is reset to 10:00 (25). This means, you can never run out of time when you play the total of 25 stones within 10 minutes.
This style has been used on IGS-Pandanet for many years and is most common. Every client supports this time system.
Byoyomi style is quite commonly used among Japanese players and in professional tournaments.
Each player starts with an initial main time and then playes one move in a given period. After the main time has run out, you get for example 30 seconds for one move. The clocks show this as "00:30 Byo". If you play your move within 30 seconds, the clock is reset to 00:30 again.
Additionally to the byoyomi time there can be overtime periods. For example you get 5 overtime periods of each 10 seconds. Then when your byoyomi time runs out, you receive an extra 10 seconds to play this move instead of losing the game instantly. However, you get this extra shot only 5 times. When your 30 seconds byoyomi time runs out without playing your move (without overtime you'd lose now), the clock switches to 00:10 (4) meaning you are using your first of total 5 overtime periods and have 4 more periods left. If you play your move now within these 10 seconds, your clock resets to the 30 seconds byoyomi time again. The next time you don't play within 30 seconds, you use your second overtime period: 00:10 (3) - you are using your second period of total 5 and now have 3 left. If you used all your overtime periods up and again don't play within the 30 seconds byoyomi, you lose the game.
Basically Overtime can be understood as extra time allowing to exceed byoyomi time, but you get this extra time only a couple of times.
Overtime is optional, if overtime is defined as zero, no overtime is used.
The Byoyomi time style was recently introduced to IGS-Pandanet and is as of writing this only supported by PANDA-Egg and glGo. This means if your opponents client does not support Byoyomi time, you can not use this system and need to use Pandanet (Canadian) time instead.
When glGo sends a match request to another player, it automatically detects if the client of that player supports Byoyomi style and presents you with a different match dialog allowing to select the time style. If the opponents client does not support Byoyomi style, glGo shows the old match dialog which only allows Pandanet style.
The PANDA-Egg client uses the term "Koryo time" instead of "Overtime".