May be you want to search for a tweet, a link, a video or a photo that one of your friends posted. Today the search in FB and Twitter are very bad, so using Google may help. Also, they may try to merge organic search results with data from your friend in order to give better results. This under the hypothesis that you may be interested more in something share by your friends than in the organic results. Nevertheless, I agree with the other reply; probably is to profile you better and give more targeted ads.

If you connect your Twitter/Facebook/etc. accounts to your Google profile explicitly then Google doesn't have to rely on discovering it on its own by other means, which probably increases the accuracy of tracking you around the internet by some small percentage.

How does that benefit you? Then Google can serve you more targeted ads.

Is that really to your benefit? No, but it is to the benefit of Google's customers--namely, advertisers.