The kind of humor often used by Ovid is verbal irony. There are examples of verbal irony in, for instance, Helen's letter to Paris in Heroides, Letter XVII:
How many youths wish for the same happiness as you, who make no advances? Or do you fancy that Paris only has eyes? It is not that you see better, but that you rashly venture more; your passion is not greater, but your confidence.
Verbal irony is when someone says or writes something that has an underlying meaning that is different from the surface meaning and different from what is expected (though it is not sarcasm, a stronger form of ironic expression that intends to cruelly injure). In the quote above Helen ironically suggest that Paris might think he is the only man alive who has eyes to see Helen's beauty with.
This ironic remark is humorous in a quietly subtle way--you'll smile though not laugh out loud--as we all understand the foolishness behind someone acting like they are the only one in the world who has some virtue or some attribute.
Much of the humor in Ovid's Amores (to take just one work of his) is sexual humor. Ovid often presents human beings whose lust leads them to act in ridiculous ways. One good example appears in Amores I.4, which opens as follows in the Anthony Kline translation:
Your husband too will be present at my banquet –
I pray it’s his last meal, that man of yours!
The speaker is so fixated on the woman with whom he is having an adulterous relationship that he actually wishes her husband dead. One way to interpret passages such as this is to assume that Ovid endorses the attitude of the speaker. Another way to interpret this passage is to assume that Ovid is mocking the speaker's sexual desperation.