Three-minutes is not a long time but when you're asked to give a three-minute speech in front of a large group, it seems long enough. The group you are addressing will be the primary factor determining the topic but there will always be a range of subejcts within that topic.
Select a topic providing interesting information of general or specific interest to the group. Consider your personal experiences, people you have met or information you have learnt. If you have just returned from an African safari, share your adventure with the group. Other informational topics include discussions on events, local authors, organisations, government agencies and personalities.
Educate the group on a subject matter within your field of experience. Give them a nugget of valuable information which will help them at work or in some other part of their lives. Consider your expertise when selecting a topic. If you have mastered a popular computer program, give the group some practical tips. As a coupon guru, tell the group ways they can save money. A speaker in human resources can give a brief speech on dressing for success, or ways to approach an interview. A real estate professional might give a brief talk on staging a home for sale, while someone in the medical field could talk on ways to find a new doctor.
Use the three-minute speech to campaign for a political office or pitch a local charity, organisation or fundraiser. It's a small chunk of time where you can introduce yourself or your cause to the group. The speaker is not necessarily the focus of the topic. For example, if the local humane society needs donations, use this time to speak about the work of the society and encourage the group to support the organisation. The speech may not support a particular cause or person but can still encourage the group to get involved or get out and vote.
Inspire the group with a motivational speech. Aim to uplift the group, to give it a more positive perspective on life and encouragement. You don't need to be an experienced motivational speaker to select this type of topic. Recount an inspirational story you have heard or experienced. This might even be a story you have read about in the newspaper.