Short answer
Mahr is the marital gift or financial entitlement agreed for the wife as part of the marriage.
Islamic Guidance
What Islam teaches
The Qur'an instructs men to give women their bridal gifts graciously. Mahr belongs to the wife and should not be treated as a payment to her family.
Practical Guidance
What you can consider
Discuss Mahr clearly before Nikah, record the agreed amount properly and make sure both sides understand whether it is prompt, deferred or structured according to the applicable arrangement.
Sources
Qur'an 4:4.