A 51% attack is a situation where more than half of the computing power on a blockchain network is operated by a single entity or group, which gives them complete and total control over the network.
Things that an entity with 51% of the computing power can do:
Halting all mining.
Halting and manipulating all interpersonal transactions.
Double Spending using singular coins over and over (this simply means that they can spend same coin/token money twice by deleting transactions from the Blockchain records).
While I am exploring the forum I found this thread and I just wanted to say that this isn't accurate in terms of definition.
A 51% attack doesn't necessarily give control of the network completely, there has been lot of instances when a single mining pool of Bitcoin network crossed 51% but they chose to be loyal and focus on the block rewards instead of tampering and altering the network.
And also about double spending the attacker can spend the coins twice but its much more complicated since it requires precision to fork the chain by creating a separate private blockchain and then quickly switch to the other branch (the longer chain) to render the original transaction invalid.