Well ,the capital city is the seat of government so government would likely be in disarray for a bit. The most important thing is the impact it would have on morale. For the attacking army, it would be a big factor in raising morale as propaganda would pounce on on the chance to spread around "we captured their capital, we captured the figurative centre of their country." On the other hand, soldiers of the side that lost their capital would know that their enemy had captured the figurative centre of their country. Morale would understandably go down.

Also, considering that capital cities usually are extremely well defended in times of war, if the enemy captures your capital, chances are that they have a large advantage in the war and will likely come out on top.

Well it's usually the seat of government. If you can take the head of state prisoner, along with any other important politicians, or military leaders, the ability of the nation to organize and coordinate defense would be pretty seriously reduced. The rest of the country would be pretty much stuck with guerrilla warfare as the remaining option unless the standing army was elsewhere and still had enough leadership to continue the war

This question was debated in depth in early 19th C Sweden after the loss of Finland to Russia left the capital, Stockholm, much more exposed. IIRC I have read a contemporary article by the Krigsvetenskapsakademien (War-science Academy) that asked, and answered the question "Is the war lost if the Capital falls". The answer was "not necessarily". As part-proof was referenced the recent events when Moscow (not formally the capital but still of central importance) fell but the war was not lost. This led the Swedes to adopt the idea of Central Defence (centralförsvar) with the policy of building powerful defences in the middle of the country. Google Karlsborg Fortress to see a truly remarkable building that came from this policy. That said the rise of railways and the way that most railways ran to nation's capitals meant that for a long time nations were far more vulnerable to the capture of the capital. had Moscow fallen in 1941 the loss of such an important railway hub would have caused the Soviets much grief. BTW and a bit off-question: A Swedish author called Frederik Böök wrote an interesting paper on the subject of railway's effect on fortifications and vice-versa. Edit: grammar and last sentence.