Last words are something that we sadly can't always control, and often are completely mundane and unmemorable. However, sometimes luck is on the side of the person and they manage to say something poignant. Regardless, last words can be something that a loved one can find comfort in during a difficult time.
Yes, the last words of people really matter to the people who care about them. Even if someone's last words are not important to society at large they may be important to the family members of the person. Furthermore, hearing people's last words is interesting to the public if the person is famous.
When a person makes a last word, it means that they have thought about what their life meant. Often times, when a person makes a last word, a person has decided what they thin is most important in life. They might want to tell other people something they want to know or make a last confession.
The last moments of a person's life may lend themselves to so many different thoughts: missed opportunities, loved ones, happy memories, unfinished tasks, religious revelations, or how much pain the person is in. Thoughts may be expressed in sentence fragments or single words, which someone else might then interpret or even misremember. Last words are often uttered when the brain's synapses are already misfiring, and usually mean very little.