MeSH is the US National Library of Medicine(NLM)'s controlled vocabulary or thesaurus of terms used to organise the MEDLINE database. It is also used for searching in PubMed, and some other databases, such as CINAHL, and the Cochrane Library.
Everything fits into a hierarchy.
For example: a search in MeSH Browser for "deep vein thrombosis" identifies the MeSH term as: Venous Thrombosis (click to see MeSH entry)
You might choose "prevention and control" as a subheading under this MeSH term and then combine it with another MeSH term. e.g.
This 3-minute YouTube video created by the NCBI is an excellent introduction to how to use MeSH to build a better PubMed query.
It is best viewed at full screen.
Davis, S.K., Stichler, J.F., & Poeltler, D.M. (2012). Increasing exclusive breastfeeding rates in the well-baby population. Nursing for Women's Health, 16(6), 460-470. doi: 10.1111/j.1751-486X.2012.01774.x
PubMed record: http://www.ncbi.nlm.nih.gov/pubmed/23253573
The main topics of the article are denoted by the MeSH terms with asterisks *.
You can see that a number of MeSH terms have been assigned, including terms with subheadings (shown after a forward-slash).
Clicking on any of the MeSH terms will bring up the highlighted drop-down list, offering to further search PubMed or the MeSH database for that term, or to add it to a new search.
While using MeSH to structure your search is an excellent feature of PubMed (and MEDLINE), be aware:
Searching with MeSH subject terms EXCLUDES in process and publisher-supplied citations, as well as other PubMed citations that are not indexed for MEDLINE (e.g., citations that are out of scope for MEDLINE, such as a volcanology article in Science). These records do not (or do not yet) include MeSH subject terms.