Truncation (or "wildcard searching") is a way of searching for variable or branched spellings of search terms.
In this case, searching for "Darwin*" means I am telling the database to search for the following terms: Darwin, Darwin's, Darwinian, Darwinism, etc.
You can also sometimes place a wildcard in the middle of a term. You may use this if you have questions about how a certain word may be spelled (think "color" or "colour").
Remember to always check the "help" or "search tips" document in the database you are using. Some databases use truncation in different ways.
Proximity searching is an extremely powerful search mechanic.
In this case, by searching for "undergraduate n5 research" I am telling the database (ERIC) to find articles that have the search term "undergraduate" within 5 words of the search term "research" in the abstract. This can be a useful alternative to running a phrase search (putting quotations around a phrase).
Remember to always check the "help" or "search tips" document in the database you are using. Some databases use proximity searching in different ways.