I’ve written about this at length, but the short version is:
- Get Robert interested in Margaery.
- Reveal Cersei’s incestuous adultery, remove her and her children.
- Pop Margaery into Robert’s bed to console him.
- Marry Margaery to Robert, produce a new legtimate line of succession.
- Replace all Lannisters in government.
As for what Renly gets out of it?
- Well, he eliminates a deadly rival in Cersei and the Lannisters, who need to have him killed along with Stannis to secure the throne against the legitimist Baratheon claim.
- Moreover, he’s in the best possible place to reap the benefits – as the man who not only exposed Cersei’s infidelity but also introduced Robert to the new hotness, Renly is likely to get richly rewarded by Robert and could very easily become the next Hand of the King.
- And even if he doesn’t get that particular prize in the moment, he’s already a member of the Small Council, and as Loras’ husbando he’d definitely be the leading force of the dominant faction in court politics (since he can run rings around Mace any day of the week).