Non-manifold:

There is a cube & three open balls. Ball 2 contains its centre on the top face. The intersection of this ball & the surface of the cube is an open disk (illustrated in red). Ball 1 contains its centre on an edge. Its intersection along with the surface of the cube is a "bent" open disk, which of course may be "unbent" to make it an open disk. Ball 3 contains its centre at a corner. Its intersection along with the cube's surface is a three-way bent open disk.

Figure illustrated a solid whose bounding surface is not a manifold. The intersection of open ball & the surface of the solid is the union of two intersecting open disks. This intersection may not be deformed to an open disk without "gluing" as a result; the surface is not a manifold.

              Figure: A Non-manifold