"I remember somebody once said that Jupiter was the second brightest planet after Venus. However, I saw in an almanac that Mercury will be brighter than Jupiter this July. How is that possible? Oh, and I gave you a made up name that you can use."

- Bertie Wooster

Right ho, Bertie!
That is an excellent question.

First, the statement. Yes, Jupiter is the second brightest planet in our sky. Venus is always the brightest and no planet will ever surpass it in brightness unless it goes supernova. ha ha ha*  Now, Jupiter is dimmer than Venus, but brighter than all the other planets, at least it is from our perspective. Therein lies the rub. Sometimes, Mercury will actually be brighter than Jupiter, as will occur this July. However, at this time, Mercury will be in superior conjunction, or on the far side of the Sun relative to Earth. When at superior conjunction, Mercury is "full," meaning that its entire illuminated side faces us. Unfortunately, as the Sun is between Mercury and Earth, those observers on the latter cannot see the former.

In July, Mercury is visible early in the month. (Consider this a preview of July's Planet Watch segment, for the benefit of those who just can't wait.) During mid month, Mercury vanishes from sight and moves into superior conjunction on July 23rd. At this time, Mercury will be brighter than Jupiter, which will remain in our western evening sky. If - and this is an impossible if, Sartre-, we could somehow turn off the Sun on this day, Mercury would appear brighter than Jupiter. Of course, Mercury and Jupiter shine by the light of the Sun, so if we
snapped off the Sun, these planets would disappear from view, as well.   

So, Bertie, there are times when Mercury is, indeed, brighter than Jupiter. However, Mercury can only be brighter than Jupiter when the former is at or near superior conjunction. As we can never see Mercury at these times, Jupiter will always be brighter than Mercury from our perspective.

I hope this answer helped.

And, if I may ask, why didn't you just ask Jeeves?!  Ha ha ha**