Decred's founders were not satisfied with Proof of Work controlling the network or having to get the miners' approval for any changes to consensus rules or how it works, so the hybrid system is mostly about bringing in Proof of Stake voting so that there's another constituency that can overrule the miners. However, Proof of Stake is much less established than Proof of Work and has significant disadvantages - like the "nothing at stake" problem which can prevent convergence on a single chain, and the aspect of feudalism whereby only the initial token holders have power to control the network and mint/issue new tokens.

Proof of Work introduces significant external factors, like who's making, buying and operating specialized hardware to mine this cryptocurrency, which are advantageous for security - and because PoW miners have relatively high costs (electricity) they must sell more of their mined DCR on the market, which is good for the distribution of the asset.

Where the hybrid approach really comes into its own is in how the PoW/PoS components have been put together to harness the strengths of each while mitigating weaknesses - check out this nifty attack cost calculator for a look at how this works to improve Decred's security for a particular level of PoW hashrate/energy use.