Andorians are the blue-skinned aliens with antennae that first show up in the original series. Fans love them, but they've been overshadowed by the Vulcans and Klingons. It's a shame, because the Andorians are the most dynamic race in the show. Other alien races are monolithic: all Klingons are violent warriors. Vulcans are stoic and emotionless. Romulans are crafty and sneaky. But when the Andorians were onscreen, they were never one-dimensional.
Andorian culture mirrors modern human culture. They are violent and use a powerful military, mostly for homeland defense. Even though they aren't above torture and extortion, it's clear the Andorians use them out of a desire to protect their homes and families. People can relate to that. Everybody has an issue with torture and war, but most people are willing to put their morals aside when it comes to defending things they love. In that way, the Andorians are more like us than the humans in Star Trek.
In Discovery's timeframe, the Andorians have already joined the Federation. Having them play a major role provides a lot of dramatic tension between an emotional, violent race and the peaceful utopianism of the Federation that would lend itself to an exploration of the more damaging aspects of modern human culture. Hard-hitting analogies always work great in Star Trek, and the Andorians would make an effective delivery mechanism. Plus, we could get Jeffrey Combs to reprise his role as an Andorian commander—win-win.