According to Wikipedia, vesting is to grant the current or future right that is immediately secured. This concept can appear in a number of contexts, but the most common are inheritance law and pension plan law.
In Steem's scope we can compare that STEEM Power (SP) token is held, locked in a contract that gives you more voting power. The more STEEM Power you have the greater Reward for Curating, Posting & Comment, your voice carries more value which means that you will give more to your users as you vote and you own when you contribute.
In the Steemit FAQ we are told that STEEM Power is less liquid. If a user wants "Power Down" SP, they will receive the same weekly STEEM distribution, over a 13-week period.
In a financial analogy, STEEM Power is basically a STEEM held in funds. Vest is part of the fund. In his explanation of the Steem Economic System, steemian 
Steemd's blockchain explorer site shows how many Vested STEEM each steemian has, visit www.steemd.com/@steemitusername (replace with the username you want to check). This is different from the Steemit Wallet, which indicates the amount of STEEM required to purchase the Vest amount owned by the user at that time. This means Vest is a small part of STEEM, very small which is usually represented with MV units (Megavest or 1 Million Vest).
What is the difference between STEEM, Steem Power, and Steem Dollars?
STEEM
STEEM is a liquid base currency token in the platform. STEEM can be turned into Steem Power, exchanged with Steem Dollars, or transferred to another account. This is a cryptocurrency token, similar to bitcoin.
Steem Power
Steem Power (abbreviated as SP) is a measure of how much influence a user has in a Steem network. The more Steem Power users have, the more they can affect the value of posts and comments. Steem Power is less liquid. If a user wants "Power Down" SP, they will receive the same weekly STEEM distribution, over a 13-week period.
Steem Dollars
Steem Dollars (commonly abbreviated as SBDs) are currency tokens with stable values designed to be pegged to $ 1 USD. Steem Dollars can be traded with STEEM, and transferred to another account for trading or exchange. Steem Dollars can also be converted into STEEM through a 3.5 day process.