I'm a beginner with databases and have been perplexed by the various definitions to distinguish these two. Various google searches have not fully clarified their differences. Please help explain them on a simple level.
A composite key is simply a key that contains two or more columns.
A surrogate key is one which is not naturally unique to the data but is added or imposed onto the data for (hopefully) a good reason. Examples can include IDENTITY columns in SQL Server - known as autonumbers sometimes in other products.
Perhaps you are storing information about people, but you can't be sure that they can be uniquely identified by a combination of their name, date of birth etc.. If you don't have some external information about them that ascribes uniqueness (e.g. Social Security Number), you can use a surrogate key to uniquely identify the rows.