Q:

Use of "conocer" in the context of meeting someone

From searching the web via Google, I'm finding that "conocer" can be used to express that one is meeting someone else for the first time.
Does this mean that two or more persons are meeting for the first time ever? Or does it mean for the first time within a particular day?

No conoció a su madre.
He didn't meet his mother.

The above Spanish is from a lesson I'm taking at Memrise.com. This confuses me because usually an individual is NOT meeting his mother for the first time ever. Why is it appropriate to use "conocer" in this context?
UPDATE: Perhaps I've made a faulty assumption here. In the example that I used, I assumed that 'his' is referring to the mother of 'he'. Perhaps 'his' is referring to someone else's mother. For example:

He (Roberto) did not meet his (Brian's) mother.

In this case, this meeting that did not occur would have been a first-time meeting.
I hope that I'm making sense here! :)

A:

Conocer, in Spanish, has multiple meanings, just like know has multiple meanings in English.
RAE lists 10 usages of conocer. The most relevant ones to your question are:

tr. Entender, advertir, saber, echar de ver a alguien o algo.
tr. Tener trato y comunicación con alguien. U. t. c. prnl.

Roughly translated:

transitive verb. Understand, notice, know, or to see someone or something.
transitive verb. Engage in dealings and communication with someone.

So the explanation is simply that the word has multiple meanings.  It can mean to know someone, and it can mean to meet someone.
Some examples of how to use conocer, and how to talk about meeting and meeting up:

¿Conoces a Maria?  / Do you know Maria?
¿Conociste a Maria? / Did you meet Maria (for the first time)?
Ayer conocí a tu jefe. / Yesterday I met your boss (for the first time).
Vamos a juntarnos en el café. / We will met up in the café.
Encontré a Maria en el supermercado. / I met/ran into/found Maria in the supermarket.
¿Conoces Ámsterdam? / Do you know/are you familiar with/have you been to Amsterdam?

A:

As a native Spanish speaker, the use of this verb often depends of context.
We can use conocer when the person introduced already knows the other.

— Hola, este es Paul.
  — Hola, ya lo conozco.

When you want to meet someone or more people for the first time:

— Quiero conocer más amigos.

When talking about knowledge:

— Conocer estas materias, ampliará tu mente.

However, we don't use conocer when we casually meet people:

— Ayer me encontré a Paul en el mercado. ( Ayer conocí a Paul en el Mercado.)

