Witch burning was indeed a pointless Muggle pastime. Sadly, the lot tend to persecute anything they don't fully understand, and witchcraft is no different. This holds especially true for the medieval era where they often hunted down anyone they wanted by using witchcraft as an excuse. Not that they were particularly good at recognizing real magic to begin with, but they also apparently made it a habit to accuse people of witchcraft that they simply didn't like. Awfully spiteful to accuse someone of a crime whose only punishment was death, don't you think.
Muggles also came up with ridiculous ways of telling who was a witch. Having a mole or distinct beauty mark could get one stoned to death. Daring to befriend a black cat or other 'unlucky' animals could get one drowned. Living alone, or enjoying a bit of herb gardening could get one burned alive. You would think Muggles would realize that with magic, a witch or wizard could easily hide these things, alter memories, or otherwise make themselves appear innocent and simply not get caught. But naturally, they were adamant that no witch could fool them and would go on burning anyone who looked at them wrong.
Occasionally, a real witch or wizard would get blamed for nonsensical things, but it really didn't matter. A simple charm or potion would keep the witch from truly burning, drowning, or otherwise being killed by the untrusting Muggles. They would simply shriek or flail about for a bit before pretending to die. After the Muggles were convinced the witch could not have possibly survived, they would just move to another village and settle back in. In fact, if they wanted to move to a new town or province, some witches would allow themselves to be caught simply to go out with a flourish. One such witch, now known as Wendolin the Weird, is said to have been burned at the stake over 47 times!
That being said, witch burning was truly just an exercise in futility that killed hundreds of Muggles and perhaps a few unprepared witches or wizards. It certainly proved that the non-magical community should not be trusted with the knowledge that magic exists.