Dower is an antiquated concept by which a wife receives certain rights to her husband’s property following his death (usually a 1/3 or ½ life estate interest). A husband’s interest in his wife’s estate is often called curtesy, and the same concept would apply. Only a few states still recognize dower and/or curtesy (for example, Ohio).
If you are in a state that recognizes dower rights, that means that both spouses need to sign any leases, even if the property was conveyed to only one of them. Additionally, a spouse should release his/her dower/curtesy interest when the property owner executes a deed.
Even if you are not in a state that currently recognizes dower, you may come across it when determining heirship based on earlier versions of intestate succession laws, so it is important to be familiar with the concept.