It is not completely clear that the personal liberty laws were important for the history of the world, but they were important for the history of the United States. They were important for US history largely because they helped to lead to the Civil War. Any impact that they have had on world history comes from the impact of the Civil War.
In the antebellum US, slaves escaped from the South to the North on a fairly regular basis. The Constitution had a provision that required that escaped slaves should be returned to their owners. As time went by, the North became much less sympathetic to the South and to slavery. Most Northerners did not believe in abolition, but they disliked the slave system and were suspicious of Southern attempts to make them help support that system.
Because of these attitudes, many Northern states passed “personal liberty laws.” These laws were designed to make it harder for fugitive slaves to be taken back into slavery once they reached Northern states. These laws infuriated the South. The South felt that these laws showed why they needed to secede from the Union. They felt the laws proved that the North had no respect for the laws and for Southern rights.
These laws helped lead to the creation of the Fugitive Slave Act as part of the Compromise of 1850. The Fugitive Slave Act was one of the most controversial laws of the antebellum era. Anger over that law helped bring the Civil War about. Since the personal liberty laws led to Southern anger and to the Fugitive Slave Act, they also helped to cause the Civil War. This makes them important in US history. In world history, they are only important in that the Civil War ensured that the US would remain united and would no longer have slaves.