Visit and meet close to each other in meaning. Visit implies that you have moved to a new location to do so.  it strongly implies spending time together in conversation, and doing a lot of works often without arrangement whereas  , Meet implies a more shared perspective and, often, prearrangement. 

They are similar but are typically used in different situations.

<hr id="[object Object]">Both 'visit' and 'meet' imply to see someone.

However, 'visit' implies one person moves to see someone (so you might visit someone in their home, city or even country).

'Meet' often suggests both people move and that the meeting is arranged (so you may meet someone at restaurant and an arranged time).

Also, sometimes 'meet' implies an initial introduction (so you might have met a close friend at University).