The first part of Edward Drea's book - Japan's Imperial Army - talks about the Meiji Restoration in a really interesting way. There are lots of reasons.

1. Inter-clan conflicts. Satsuam, Choshu and other domains in south Japan didn't like the Tokugawa shogunate very much. Centuries before, some daimyo had been on the losing side of the the Battle of Sekigahara in the 1600s. They'd essentially been exiled to southern Japan and given poorer lands, while the Tokugawa loyalists got better lands. The losing clans had lost money and political power. By the 1860s, they were sick and tired of being sidelined and they saw a palace coup/rebellion as a way to return to power.
2. The shogunate's weakness against foreigners. The clans that back the Emperor wanted Japan to be strong and revitalized. We think about them being "anti-Western.' They were and they weren't. Although some of them said, "Sonno joi " or "Revere the Emperor, Expel the Barbarians," they were willing to get help from foreign traders and advisers. But they felt like Japan was getting shoved around by the West. For example, the British had bombarded of Kagoshima after not getting reparations when a British citizen was murdered. The shogunate hand't been able to do anything to fight back. By getting help from the West to make Japan strong, the Emperor-supporters thought they could protect Japan from further Western incursions. It might seem turned around, but there was some logic to it.
3. Reverence for the Emperor. A lot of the more senior people leading the rebellion were pretty much using the teenage Emperor as a puppet. But a lot of samurai really revered the Emperor - when the Emperor gave them a banner during the 1860s civil war, it encouraged the people fighting for his army quite a lot! So fighting for his side seemed like the right thing to do.
4. Jobs. Lots of samurai were "ronin," samurai without a master. Fighting for the pro-Emperor side was a chance to get paid and to fight. Samurai. In the peaceful period of the shogunate, Japan had been pretty peaceful. A lot of warriors felt adrift and without purpose. War gave them that purpose they wanted.

Can you just clarifying which conflict you mean by Meiji Uprising so I'm answering the right question?