An exploit takes advantage of a vulnerability in order to access or infect a computer.
Usually an exploit takes advantage of a specific vulnerability in an application and so becomes obsolete 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 ensure your anti-virus or endpoint security software is active and your computers are fully patched. Buffer overflow protection (BOP) technology can provide effective protection against many exploits. Client firewalls are a first defense against many exploits and should be deployed throughout an organisation, not simply on mobile assets.