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?