Masternodes are the servers running the full dash wallet and make decisions, such as locking transactions with InstantSend, coordinate mixing of coins, and voting on budget proposals. Masternodes are required to have 1000 Dash collateral, a dedicated IP address, and must run 24/7 in a stable enviroment. Masternodes get paid a rising half of the new block reward. Actually the minimum reward of ~1.38 dash is paid to each Masternode each 7 days.

Masternodes enable the following services:

• InstantSend (instant transactions based on LLMQ). In contrast, Bitcoin takes about 10 minutes to confirm a payment.
• CoinJoin (private transactions). In contrast, Bitcoin transactions are totally public and traceable. Only the identity of the addresses is anonymous.
• Decentralised Governance (masternodes govern, while the blockchain funds development). In contrast, Bitcoin is controlled by a few big miners and funded by 3rd party centralised institutions with self interests.
• Dash Evolution a decentralized payment processor (think a decentralized Paypal).
• ChainLocks is a feature to protect from 51% mining attack.

Masternodes are also given voting rights on proposals. Each masternode has 1 vote and this vote can be used on budget proposals or important decisions that affect Dash. For a complete list of current proposals please click here.

Having the Masternode let you earn about about 7% a year in Dash rewards where you receive them in less than a week actually and  get them directly at your dash desired address. However having an Evonode let you earn close to 14% APY but the collateral is of 4000 Dash.
This reward falls off in subsequent years but as the value of Dash tends to rise and the supply of Dash goes down, masternodes should still be sufficiently incentivized.
This projection also doesn’t count the fees that masternodes earn whenever someone uses its services (InstantSend and CoinJoin).
Check here to see how much can you earn now.