There were two schools of thought in Jesus' day concerning divorce, one liberal and one conservative. Rabbi Shammai taught that divorce was only permissible on the grounds of some sexual impropriety. His was the stricter view. Rabbi Hillel, on the other hand, had a more liberal view and taught that a man could divorce his wife for any reason. If she burned his breakfast, put too much salt on his food, showed disrespect to him, spoke disrespectfully of her husband's parents in his presence, spoke to a man on the street, or even let her hair down in public, he could divorce her. The view of Rabbi Hillel was the view that was popular in Jesus' day. So divorce was common in Palestine, and in this respect the setting was not unlike our own.
Perhaps the most significant difference between their customs and ours lay in the status of the different genders. A man could divorce a woman on a whim, but a woman could not divorce a man for any cause. The Old Testament contains a highly patriarchal position that viewed a woman's sexual immorality more as property damage against her husband (or her father) rather than as a moral issue. A double standard shines throughout the Old Testament, where it was not uncommon for the male rulers to have many wives and hundreds of concubines. If you look carefully at the question of the Pharisees, you will find no concern whatsoever about a woman's rights in marriage or divorce. "Is it lawful for a man to divorce his wife?"