Kurt Angle and John Cena had a couple of feuds during the 2000s. The first one was in 2003 when John Cena was a heel and that was the last time when we saw John Cena playing a heel character, unfortunately.
The second feud between John Cena had been the controversial one which we are talking about here. It was in 2005 when WWE was trying to build John Cena as the face of WWE. After Cena won the WWE Championship from JBL at WrestleMania 21, he defeated JBL for a number of times more and got drafted to WWE Raw for the first time in his career.

Triple H Tried To Bury Kurt Angle Once? – Angle Reacts
After coming to Raw, Cena first had feuds with Christian and Chris Jericho. The feud with Chris Jericho continued till Summerslam of that year and Cena came out victorious on all occasions.
Then Cena’s feud with Kurt Angle started. The feud kept on going for five long months and the sole purpose of this feud was to hype John Cena only. However, there are some controversies that Kurt Angle could not push Cena as WWE wanted him to. Angle was unable to gain the heat from the crowd to push their main babyface which Triple H did not like. And he wanted to bury him.

But these remained only rumors before Kurt Angle recently talked about these rumors himself on The Kurt Angle Show. He said;
I didn’t hear anything backstage of Triple H burying me. He’s entitled to his opinion, I can’t do anything about that. I don’t agree with him, I think John Cena, when he came up through the ranks when he started, he was booked as invincible, he hardly ever lost. [WWE] did the same thing with Roman Reigns and look what happened to him, it took a long time for the fans to get with Roman.
The fans are a bit rebellious, they don’t want a guy that’s dominant or invincible. They want a guy that’s vulnerable that could win or lose at any time and John was always booked to win.

Triple H and I were veterans, better known at the time. Cena was an up and coming talent so they were able to recognize us as more formidable opponents and the more popular wrestlers. It’s an uphill battle for John because they booked him so quickly into the main event as a baby face, that’s really hard to do. Triple H and I being the more experienced veterans, people knew us.
As we all know, Triple H is not the type of person who would want to bury anyone intentionally. Yes, there are many rumors of Triple H burying a lot of talents during his prime days like Booker T in 2003, but these are only rumors. Nowadays we can clearly see how Triple H is trying to promote new talents and kudos to his efforts really.
Credit: The Kurt Angle Show. H/T WrestlingInc.