That is a bog-standard electrolytic capacitor.
The orange crust is the dried out liquid electrolyte from inside the capacitor. That kind of capacitor is designed with pleated seams in the top, and is meant to pop open if it gets too hot inside (which makes the electrolyte boil/decompose and release gasses, that would otherwise build up pressure until it explodes like a bomb). Leaking/spewing orange spooge all over is a common problem with electrolytic capacitors, especially on older boards from the late 90s to early 2000s. See also "
Capacitor plague". That board is probably outside the era when this issue was most prevalent, but any old electrolytic cap is at risk of this happening.
You can buy them by the jillions from places like
mouser electronics.
You need the numbers on the side of the can-- the voltage, and the discharge peak in uF. (it can also be pF for very small ones) Ex-- "5v 2000uF"
Replace it with a like-spec'd lytic cap.
You need to neutralize the spooge that came out, and do it quickly. It is corrosive, and will damage the circuit traces of the motherboard if it gets underneath the solder resist mask. It is an alkaline solution in the capacitor, so use a weak acid, like lemon juice or vinegar. Let it just sit on top of the spooge mark until it stops making bubbles, wipe it up with distilled water, then dry it with 99% isopropanol.
See also, this lovely video from Adrian's Digital Basement, where he recaps an old macintosh board. (that suffers capacitor plague.)
https://www.youtube.com/watch?v=e-1l6zh4K8UYours should be easier to do, because the cap is NOT surface mount.
When replacing the capacitor, be sure to annotate on the board the orientation of the marked leg. Bad Things Happen when you install them backward.
As for what capacitors DO-- They retain a small voltage that is applied, and then release it after the current is stopped. They are frequently used to buffer and filter power rails to level out voltage levels. This is especially true with AC power circuits. (See also, related issue "
Rifa Capacitor", which is pretty exclusive to old linear power supplies from the 80s.)
Frequently, similar circuits are used on the motherboard to balance out/filter noise generated by the microwave frequency devices in a motherboard. (such as noise generated by north and south bridge chips) See also, "
DC noise filter circuit" These are especially common on the 5v power rail that supplies power to the card slots on motherboards, and they are typically situated very near the ATX power input connector. they are comprised, usually, of a beefy 5v electrolytic capacitor and an inductor.