Well, one explanation is we tend to notice what we think of and think of what we notice. Since you made the association with the number and your age, you're liable to notice it more.
However, since you'll be turning 34 soon and seem concerned about the implications, perhaps it's a message to not worry at all about turning 34.
3+4=7, so the message may be that you have some wonderful gifts just waiting to be accessed and they'll be more accessible to you very soon. 7 is the number of the number of the mystic as it's both spiritual and intellectual. 7 also denotes a healthy accurate intuition and reflects philosophy, idealism, magic. How often have you heard of "lucky number 7"? There are 7 ancient wonders of the world, 7 days in a week, in fact, 7's figure prominently in spiritual and even some philosophical writings.
Or, maybe you're being told to trust your instincts and to not fear growing older. With age comes wisdom. ;)