A non-maintainer upload (NMU) is an upload of a package to the debian archive by a developer who is not the maintainer of the package. This should usually not be the case, but in special cases (such as for RC bugs, when the maintainer does not respond to the bug report) it is allowed.
In a "normal" non-maintainer upload, for a non-native package, the second-level version number in the Debian revision is created (or bumped, if it already exist). For instance:
1.2.3-1 -> 1.2.3-1.1 0.5-2.1 -> 0.5-2.2 0.6-3 -> 0.7-0.1 # if the NMU is of a new upstream version
Binary non-maintainer upload
For more detail, please see the binNMU page.
A binary non-maintainer upload (binNMU) is the upload of a binary-only package. This is necessary when the build for a specific architecture failed, or produced buggy packages, due to an error in the build environment itself (not due to an error in the source package).
The package gets a new version number which is the old version number with the suffix +b appended plus a version number for the binNMU (e.g. version 2.3.4-3 will become 2.3.4-3+b1). The only file which is modified in a binNMU is debian/changelog which gets a new entry for the new version.
When a source package produces multiple binary packages, its maintainer has to take some care to ensure that a binNMU will not break dependencies between these binary packages. For more detail, refer to the binNMU page.