<em>Saber</em> and <em>conocer</em> both mean "to know" but in different ways. <em>Saber</em> means "to know information," like you know how to speak English or how to draw or what an apple is.
<em>Conocer</em> means "familiarity." So you're acquainted with a neighbor or the city of New York. You use the personal <em>a</em> with <em>conocer</em> when you're expressing that you're acquainted with someone.
For example, <em>Conozco a Maria.</em> (I know Maria).