When you steal someone's thunder, you win praise for oneself by stealing someone else's attempt to impress. Neat could mean "tidy", but I'd need more of the sentence to figure it out.

Usually "steal your thunder" means to take someone's glory. It's an expression that is used when you take attention away from someone's achievement or news by saying something more exciting or great. An example might be "I didn't announce I was pregnant at her wedding because I didn't want to steal her thunder" implying that saying you're pregnant would take attention away from the marriage. Neat can mean tidy, but it is also a slang word to mean "cool" like "that's neat."