to wait (for), to wait and see, to await
[af-wach-ten, wacht-te af, af-ge-wacht] 

‘Afwachten’ can be used as an alternative for ‘wachten op’ but typically only when it regards a moment in time (that you are waiting for to arrive). Its usage usually implies that you will wait for that moment ‘patiently’ and that you are not anxious (the latter may be the case when using ‘wachten op’). When you are, however, waiting for an outcome of an event and there is some uncertainty around the outcome, or you are postponing another decision until the outcome of the event is known, it is more common to use ‘afwachten’ instead of ‘wachten op’.

“En nu?” – “Nu wachten we af!” 
(“And now (what do we do)?” – “And now we wait!”)

“Prima, ik wacht uw reactie af en dan spreken we elkaar te zijner tijd.” 
(“Excellent, I’ll await your response and we’ll speak again in due course.” Note the use of ‘te zijner tijd’: in due course / when appropriate.)

“Kalm wachtte de leeuw het juiste moment af om toe te slaan.” 
(“Patiently the lion waited for the right moment to strike (hard).” Note the verb ‘toeslaan’: to strike (hard), to attack.)

“De zebra op zijn beurt keek de leeuw afwachtend aan…” 
(“The zebra, in its turn, looked at the lion with anticipation….”)

“Is goed, we wachten de bui nog even af, maar dan komen we op de fiets naar de stad, tot straks!” 
(“Alright, we will wait for the shower to pass over, but then we’ll come to the city centre by bike, see you soon!” Note ‘naar de stad’; here ‘de stad’ refers to the city centre (there where typically the action takes place).)

“Ik moet het resultaat van de onderhandelingen nog afwachten, maar ik heb goede hoop dat het huis volgende week verkocht is.” 
(“I still have to wait and see what the result of the negotiations will be, but I am hopeful that the house will be sold next week.”)

Related words:
–  (iets) Tegemoet zien: to await/face (something), to look forward to (something) [verb] [zag tegemoet, tegemoet gezien].
– Wachten (op): to wait for, to await [verb] [wachtte op, op … gewacht].