It's the Spanish personal "a" which is placed between the verb and the direct object when it's a person. It has no equivalent in English! Example: Vedo a Maria. When you have a masculin article you can combine a + el => al. Example: Vedo al maestro. With a feminin article it stays unchanged. Example: Vedo a la mestra.
Yes, "conocer" = "to know".
In English, when you want to know someone you can also say that you want to meet with that person. This "equivalence" works for both English and Spanish.
But, there's a catch: in the sentence "I want to meet you again tomorrow", you cannot replace "to meet" with "to know" and the same applies in Spanish.
Hence, the equivalence exist but it is not always correct.
My personal opinion, teaching that "conocer" = "to meet" is dangerous.
It might be just me, but to meet isn't anything like as in depth as to know. Getting to know someone is not the same as simply meeting a delivery driver for example. Not saying it's wrong, but just seems like putting meet as an equivalency to know is over stretching its meaning.