What's wrong with the words "wife" and "husband"? Why do people instead use "partner" more and more often?
The short answer is that it's all-inclusive - it avoids any labels of gender, marital status or sexuality.
Also, in this day and age, not all couples decide to get married (and unfortunately, in many countries, couples in homosexual relationships don't have the option to get married), so the term 'partner' can seem more appropriate to some in terms of describing the stage of the relationship. Imagine a couple from the scenario above, who can't, or chooses not to get married. Boyfriend or girlfriend can imply a less serious relationship. 'Partner' implies a more permanent state.