I think this is an explanation that can be understood easily:

http://magyarora.com/magyar/grammar.html - It's right at the beginning.

Várok means "I'm waiting" and Várom means "I'm waiting for something". For example: Várom a buszt. is "I'm waiting for the bus." (The -t at the end of busz indicates that it is the object.)

It is one of the most difficult thing to explain to a not native Hungarian. Most of natives doesn't know why they use (Its name is "alanyi és tárgyas ragozás")

Várok: I am waiting for something to be happened.

Várom: I am waiting for a specifien thing. (I am waiting for the bus)

Check this:

https://www.mozaweb.hu/Lecke-MGY-Anyanyelv_felsosoknek_6-Az_alanyi_es_a_targyas_ragozas-98631

Hi! A few sample sentences, so you can understand the difference:

A barátomat várom. - A barátomra várok.

Régóta várom a barátom. - Régóta várok (itt).

Várom, hogy megérkezzen a barátom. - Várok a barátom érkezésére.

Hope this helps.