How to best motivate your talk will depend on the kind of material you want to present. Firstly, ask yourself why should the content of your talk interest the public. Is it because it is related to some well known problem or theorem that everybody is interested in? Then start your talk by talking about that problem or theorem, and then introduce your work and show connections. Are you about to present research that brings a breakthrough in an area where other people had worked with less success than you? Then start your talk by introducing the problem and stressing how hard it is by listing the results of those people; then try to impress them with your result. Or did you just invent some interesting new concept? Try to motivate it e.g. by showing examples that indicate that this concept fills an important gap. In any case, it is better to start your talk with a nice and elementary problem that will automatically attract everybody's interest than with a 4-line theorem or definition.
Having these naive examples in mind, the best thing to do is use your imagination when looking for a motivating introduction.
A. Georgakopoulos: How to give a talk that is not too bad.