1. Delegated Proof of Stake (DPoS)
Proof of Delegates is the consensus algorithm used by Rise. It combines elements taken from the Proof of Work (PoW), Proof of Stake (PoS), and Delegated Proof of Stake (DPoS) consensus algorithms.
The Rise network is secured and/or protected by 101 active delegates. Each delegate is elected by the stakeholders of Rise. Once voted into the list of active delegates they are given the authority to generate blocks. Every Rise stakeholder can be a part of the electoral process, by placing votes for delegates in their favour, or by becoming a candidate themselves.
The duty of the 101 active delegates is to secure the Rise main blockchain (i.e. the mainchain). In order to provide an incentive to secure the network, transaction fees on the network are distributed equally amongst the 101 active delegates. In addition, an inflationary block reward (aka forging reward) is distributed to each block generator.
2. Benefits of Delegated Proof of Stake in comparison to PoW/PoS
Every blockchain based crypto-currency to date, uses a consensus algorithm in order to determine who will generate the next block.
Bitcoin introduced Proof of Work (PoW) from which miners have to calculate a solution (hash) to a problem, wherein the more powerful the miner is the faster he can find that solution. The miner who finds the solution first, mines (generates) the block, and a specific amount of Bitcoin along with it. That means the miner has a financial incentive to be the fastest. Therefore, Bitcoin has an ongoing arms race to become the most powerful miner, leading to an ever increasing energy consumption of the whole network.
Nxt introduced Proof of Stake (PoS) which removed the mining element from the network, thus reducing the energy consumption dramatically. With Nxt, your stake, i.e. the amount of coins you own, determines your chance to forge (generate) the next block. Therefore, there is not an arms race as such, but rather an emphasis on increasing your NXT stake, in order to increase your forging chance. However, in comparison to Rise, the Nxt forging rewards are negligible.
Rise combines both worlds; the energy friendly Proof of Stake (PoS) algorithm, with the competitive element of Proof of Work (PoW). Additionally, Rise adds a community element of elected delegates to the consensus mechanism.
3. What are the drawbacks of DPoS?
Having a fixed amount of active delegates may result in a less decentralized network. Ideally, the community aspect of the network should fix that issue. If only a small part of the Rise users vote for delegates this problem becomes worse. In the future the number of active delegates can also be increased, if the demand for it is there.
The DPoS variant of Rise also introduced inflationary forging rewards in order to have an incentive to become a delegate. While this is no real drawback some might have concerns over an inflationary crypto-currency.
Daniel Larimer, founder of BitShares and DPoS, argues that 101 single-purpose servers are more decentralized (and cheaper) than a thousand or so miners on a few mining pools. 
Already, Bitcoin is centralized to the point that with just three mining pools, you can control 51% of the network. With just four ASIC chip manufacturers, you can control 90%+ of production of future hashing power.
Vitalik Buterin, founder of Ethereum, calls our type of blockchain a consortium blockchain. 
I think it is incorrect to say that [a consortium blockchain] is centralized […]. Realistically, it is secure enough; it is decentralized enough. And it does provide fairly strong security assurances by itself.
This article uses the Lisk Wiki on GitHub as basis.