A band-aid is a small covering placed over small cuts to protect an injured area, limit bleeding, and speed healing. Properly speaking, Band-Aid is a brand name, but is so widely known that it has become an idiom in itself.
A band-aid solution is a quick fix incapable of dealing with problems of a large scale, providing temporary relief only, and usually, inadequate temporary relief at that.
Example: "Education is in crisis. What we need is comprehensive reform, not band-aid solutions that won't work and only delay the inevitable!"