A application exploit is when hackers takes advantage of a vulnerability inside of an application order to access or infect a computer.
Usually an exploit takes advantage of a specific vulnerability in an application and becomes ineffective when that vulnerability is patched. Zero-day exploits are those that are used or shared by hackers before the software vendor knows about the vulnerability (and so before there is any patch available).
To secure against exploits, you should make sure your antivirus or endpoint security software is active and your computers are fully patched. This includes the operating system (OS) as well as applications.