Short answer
Compatibility includes areas such as faith, character, values, expectations, lifestyle and the ability to live together respectfully.
Islamic Guidance
What Islam teaches
Islam gives importance to religion and character while allowing people to consider practical suitability.
Practical Guidance
What you can consider
Discuss religious practice, family expectations, finances, education, work, children, residence and communication styles before marriage.
Sources
Qur'an 30:21; Qur'an 49:13; Sahih Muslim.