Since Masternodes fulfill special functions for a cryptocurrencies network but do cost money and effort to operate, they are incentivized by gaining a share of the block rewards in their respective cryptocurrency. Hosting a Dash masternode generates Dash, a MUE masternode generates MUE. The yield varies primarily according to the masternode count and each coin might have different payout periods. PIVX pays out daily; Crown pays out several times a day. This makes masternodes a form to earn "passive income" on cryptocurrencies without having to run expensive mining equipment.
Anyone can run a Masternode. The objective is to have enough of them for decentralization so nobody controls an important fraction of Masternodes. However, there is one condition that usually has to be fulfilled: You have to stake a certain amount of coins in your masternode. Staking in this context means you lock up the coins for a fixed amount of time (think fixed-term deposit). The coins don't need to be in the Masternode, but they need to be kept in a certain way. If the owner moves or spends those coins, the Masternode stops working. This "proof of ownership" system serves to incentivize masternode operators and to prevent certain individuals to control a large share of the network by themselves.