Definition: A retweet is when someone republishes or forwards a post to their own Twitter followers. Retweets are typically credited to their original authors, incentivizing users to create shareable content that expands their Twitter footprint.
If someone retweets your message, it's common practice to reciprocate with another unrelated tweet, direct message or, if you haven't yet, follow. The latter is often the easiest method if you get a lot of retweets, since responding to each individual tweet is cumbersome. You could also add them to a list for future marketing purposes, or retweet something of their's in return. For retweeters, one unspoken rule is to attach a comment to the retweet so you're adding value rather than piggybacking on someone else's work.
It's a good idea to keep track of retweets, both those that have reshared your original tweet and popular ones that are currently trending. You can see the former under your Notifications tab, while you can get a gauge of what retweets are popular by looking through your network.
Both will help you better position your branding and social media strategy going forward. Seeing which of your tweets make for particularly successful retweets will give you a better idea of what interests and engages your target market so you can replicate it in future. Knowing what retweets are popular should have a similar effect on your marketing strategy.
Retweets are also an important metric of your social media strategy's success. Many businesses will look at the amount of followers they have as an indication of how well their marketing is doing. But having a gargantuan amount of followers is no good if they're passive and don't engage with your company. If your tweets consistently get a lot of retweets however, and consistently, this tells you that what you're doing is having an impact on your target market.
Remember that this is just one metric, however. Retweets won't tell you if your social media campaign is generating sales or leads, which is significant given that a 2014 report from Webmarketing123 found lead generation was by far the top objective in digital marketing. To truly get an idea of your ROI, you have to examine many different statistics rather than relying on a single one.