A daily scrum is also sometimes called a stand-up. The reason is obvious: The participants have to stand. Why is this?
Easy question, easy answer (like many things in Scrum): We stand up to keep the meeting short.
This is because the Daily Scrum is intended to elicit the answer to 3 specific questions from each team member, and no more. Frankly, when people are sat down they have a greater tendency to waffle. Standing up leads to less waffling and keeps the meeting short and to the point. It's all about being productive and useful.
A little backup from people who have experience of a lot of meetings:
"...it’s very rare that a meeting on a single topic should need to last more than 5-10 minutes. If you stand up, you’ll find that decisions get made pretty quickly, and no one nods off! Plus it’s a great way to fit in a bit of exercise and stay focused on a busy day. "
The Wall Street Journal:
"Stand-up meetings are part of a fast-moving tech culture in which sitting has become synonymous with sloth. The object is to eliminate long-winded confabs where participants pontificate, play Angry Birds on their cellphones or tune out. "
"We stand up to keep us on focus, no sitting down. When we sit down, we start stalling.....The point is to come together very focused, just a short period, and let people get right back to work. No delays."
Hopefully this makes it nice and clear for you: Sitting down during a daily scrum = bad, standing up = good.
(Of course, there's a lot more to the Daily Scrum than just standing, and a good place to start is with this guide to daily scrums from Agile coach and practitioner +Jason Yip.)