To appraise is to estimate the value of something, but remove the second "a," and you have apprise, which means "to tell." If you hire someone to appraise your house, you might have to apprise your family of the fact that you now owe the bank more than your house is worth.
Appraise sounds like "a praise," which is what you hope for when someone appraises you or your three-story colonial. The crystal ball is cloudy, but appraise probably comes from Middle French (apreis-) and Late Latin (appretiare), meaning to estimate the value or quality of something, such as a house, an employee's performance, or your grandmother's owl pin. Here are some appraises from the world:
The cancelations reflected mortgage applications that were refused or because appraised home values were coming in below the sales price, the group said. (Business Week)
Treasure Hunters Roadshow is visiting El Paso this week appraising all kinds of collectibles. (Treasure Hunters Roadshow)
You can see an etching of the event: King Kalakaua in white tie and tails, appraising a long banquet table. (Washington Post)
Apprise comes from the French apprendre, to learn or inform via the Latin apprendere, to learn. These days apprise means to inform or tell. These examples will apprise you of how to use it:
When asked whether transit officials were apprised of complaints made via 311, the city's help line, Mr. Prendergast struggled to answer. (New York Times)
He took responsibility for not keeping Mr. Bloomberg sufficiently apprised of the cleanup effort. (New York Times)
To keep it straight, if your boss appraises you, you hope for praise! If you apprise someone of a situation, you might also have to advise her on what to do. Apprise — sounds like "a prize" — has another meaning, too, which is to gain in value.