What is a concealer? What is a primer? Recommendations for foundation - liquid or powder? brand?

So I currently use a simple mix of powder foundations and a MAC finish powder. Under my eyes I use ALL powder, but it looks so powdery! What do I use to get rid of dark circles without having to deal with clumpy looks? What is a concealer? or primer? recommendations for foundation? Maybe brushes? Brands? THANKYOU