The balance between under-reacting and over-reacting to a novel viral outbreak is always a tricky one for public health officials to manage. However, research on the 1918 influenza pandemic has shown that communities that enacted early social distancing measures, enacted multiple strategies (quarantine of suspected contacts and cases, isolation of the ill, school closings, public gathering bans, closing theaters, etc.), and kept them in place for longer had lower epidemic mortality curves than communities that did not. In addition, flattening and spreading out the curve, as Angelo posted, has the added benefit of helping to prevent a surge of cases that can overwhelm hospitals and other healthcare facilities, which still have to deal with other daily health emergencies.
Non-pharmaceutical interventions are like Swiss cheese: each individual one has holes in it, but if you layer them properly you can help prevent those holes from going all the way through.