The phrase itself can be used as a noun, verb, or adjective, and defines something that is very obviously forcing an image onto its observer. This can be presented in a number of ways, including:
1) A person trying to convey an image that is unlike his or her actual self typically through large amounts of makeup
2) Something, such as a television show, attempting to mimic a more popular counterpart.
Amy is a Trying Too Hard; She's wearing a shirt meant for a 15-year old. It's too bad she's very obviously in her 40's.
Adam is Trying Too Hard to convince us that he's slept with Amy, the class whore.
Mission Hill is Trying Too Hard to be King of the Hill, as evidenced by its very title.