I looked over an article released in 2003, in the very early days of MODS and METS, which outlines their basic structures and functions.
MODS (Metadata Object and Description Standard) was developed as a sort of MARC-lite schema – somewhere between Dublin Core and MARC in complexity. Although its semantics are the same as MARC, MODS uses language based tags (easier for people to understand). Although it doesn’t convert perfectly to MARC, its tags generally should map well. It is a good option for original resource description that is fairly compatible with other schema.
METS (Metadata Encoding and Transmission Standard) is an XML document for packaging a digital resource’s metadata. It is composed of six modules that point to different types of metadata, though only two (header and structural) are absolutely required. The descriptive module is the part that holds the information librarians routinely work with – the records, cataloging, etc. It can facilitate use of multiple schema (including MODS).
I haven’t researched changes that the intervening years might have brought (which might be a future blog post to look into), but the basic guidelines included in the article were very useful to look at. Reading the original intentions and structures of MODS and METS gave me a basic knowledge of what they are and how they work, while the example projects mentioned showed me some practical applications of the standards.