What happened to lead to the impeachment but not conviction of Bill Clinton?
What happened was that President Clinton lied to a grand jury. This led to him being impeached. He was found not guilty largely because enough Senators believed that the impeachment was politically motivated and that his actions did not warrant conviction.
Clinton allegedly lied to the grand jury about a purely personal matter. He allegedly lied about whether he had had sexual relations with a woman named Monica Lewinsky. He was therefore impeached for having committed perjury. But the lies he allegedly told had nothing to do with his conduct as president. For that reason, the Senate did not vote to convict him in sufficient numbers. They needed a two-thirds vote to convict but neither of the charges against him was able to gain more than a 50% vote to convict.