Since Reuben, Simeon, and Levi had committed actions which disqualified them from the top spot, the leadership position went to Judah. His name means “praise,” so Jacob was making a little pun in verse 8. His tribe will be the preeminent one above all others, even to the point of them “[bowing] down to [him].”
Let’s skip ahead to parts which might seem mysterious, but shouldn’t be. Verses 11-12 are all symbolic of prosperity and (as a corollary) victory over their enemies. As long as you get that, you get the main point of the imagery there.
Verses 9-10, however, are extremely meaningful to us as modern-day believers. Verse 10 is prophecy that Judah will be the royal tribe, and every legitimate king came from that line. The reason that this is so important, however, is because the ultimate fulfillment of these verses is found in Jesus Christ. The first part of verse 10 says that the tribe of Judah will continue producing kings “until he to whom it belongs shall come and the obedience of the nations shall be his.” In other words, one final King will come, and he will (rightfully) take over the world. All nations will bow down and obey him, either willingly or unwillingly.
As for verse 9, this was the start of Judah as the “lion” tribe. The traditional symbol of Judah was a lion (they had it on their standard), which got its start in this verse. In Revelation, however, our Lord is introduced as “the Lion of the tribe of Judah.” What Judah (as a tribe) was in part, Jesus is. He is truly the Praise of Israel.
Lord Jesus, I praise you for being the Lion of Judah. The obedience of all nations belongs to you, as well as my own. Help me to bow.