I've read that slaves were allowed to save up money from their crafts to buy their freedom. Why were they allowed to do this? As they were slaves, wouldn't their masters just take all of the money that they made?
Are you talking about the colonial US?
There were laws in different regions allowing slaves to earn some money. For example, in Louisiana, slaves had Sunday off and could keep money earned then. This still benefitted masters because slaves usually used funds to buy necessities that otherwise the master would have to provide, like clothes.
Slaves were a form of investment for masters. This meant that many slaves were usually able to make money many times their worth. The prospect of freedom could be a sort of motivator for slaves. If the slave did his normal required tasks well, then he might be allowed to go and sell some produce or other goods at the Sunday slave market. The amount of time it took for a slave to gain his master's trust to go to the slave market and save up enough money in order to buy his/her freedom ensured that the slave would pay for themselves many times over in terms of the value of their work. After they were freed, many slaves would continue to work for their former masters and while they were now being paid, they continued to help their former masters make money. Not many masters saw slavery in this light so emancipation rates remained low.
Source:
Carretta, Vincent. Equiano the African: Biography of a Self-Made Man. Athens, GA and London: The University of Georgia Press, 2005.
Equiano, Olaudah. The Interesting Life and Other Writings of Olaudah Equiano. Edited by Vincent Carretta. Electronic Edition. New York: Penguin Books, 2003.