The Custom Combo (or “Original Combo” in Japanese releases) is a system that allows the construction of combos not normally allowed; it has its origins in Street Fighter Alpha 2.
To some level, the custom combo system allows you to put together combos as you like. It is found as a system in Street Fighter Alpha 2, Street Fighter Alpha 3, Capcom vs. SNK 2, and Capcom Fighting Jam. Similar systems may be found for specific characters, such as Yun and Yang’s Super Arts Gen'eijin and Seiei Enbu.
Other systems that allow greater flexibility in combos include:
When you have accumulated enough power in your meter (which amount will vary from game to game), it will become possible to activate the custom combo.
Once you activate it, the meter you have accumulated turns into a timer that starts to count down; during this period, it will become possible to cancel from any move into any move (though there will be quite a bit of damage correction).
During this time, you will be unable to block; once enough time has passed or you get hit, the custom combo ends.
There is a long-lasting invincible hitbox at the moment the custom combo is activated; it can be activated on the ground as well as in the air, so it is possible to use for stuffing, anti-air, and jugglers, as well as a tricky anti-anti-air technique (in that activating the custom combo for the invincibility basically renders anti-airs defenseless).
Other details differ from game to game.
You cannot block while the custom combo is active, so small mistakes are highly punishable, but it is useful for both offense and defense, so if you master it, it becomes a powerful weapon. On some characters, custom combos can do nearly 90% damage out of the opponent character’s life, so the consequences of its existence should not be underestimated.
The Custom Combo system is among the the major balance-breaking issues in Alpha 3 and CvS2 (among things like landing cancels and roll cancels); particularly in Alpha 3, custom combos make it extremely easy to guard crush due to a bug.
In many cases, the custom combo itself is tough to perform, so while there are characters for whom the effectiveness of higher-level Super Combos are better and those for whom the custom combos are weak, overly strong custom combos are too low-risk and high-return, even though the person who does them may have to work very hard at it.
Needless to say, the opinion of Capcom fans is divided on the issue.