The short answer is status.

The introduction of the edited volume The Patron's Payoff: Conspicuous Commissions in Italian Renaissance Art, which I recommend, notes that to understand patronage you need to understand economic and social mobility. Reputations were based on religious piety, wealth, as well as artistic and engineering creativity. Communicating status itself has diverse purposes, from consolidation of power to ensuring a future for the family's name. Demonstrating your status was a good way to rally political support and show strength, while also showing the citizens that you care about the common good by beautifying the city. The Medici gain power, but they were a new family of humble origins: their political sustainability depended on support and reputation. Patronage is also part of what we call "the economy of salvation," meaning that by being a patron of churches and religious art, you were able to clean your soul from the sin of usury (moneylending).

You can also check out Dale Kent's Cosimo De' Medici and the Florentine Renaissance, or the 4-episode PBS series The Medici: Godfathers of the Renaissance, which is pretty accessible and informative and it's on Youtube.