Hungarian present and future tenses are about as identical as simple future, present continuous and present simple in English... Given the right context, any of these can refer to future. Since there are less verbal structures in Hungarian, it's just somewhat more common that a present tense conjugation happens to cover futural semantics (as well).
It technically means both.
The term usually means to wait for a bit of time, but the verb can be used for people and objects as well:
"I'll wait for a little bit of time." = "Várok egy kicsit." / "Várok egy kis ideig."
"I'll wait for a little one (person)." = "Várok egy kicsit." / "Várok egy kicsire."
"I'll wait for a bit (of cake)." = "Várok egy kicsit." / "Várok egy kis tortát." / "Várok egy kis tortára."
Also note that for objects, the accusative case ("várni valamiT", "várok egy kis tortáT") can also mean to expect something.