(please) try to; (please) look
A soft, encouraging way to tell someone to try doing something or to look at something.
てごらん is a friendly, casual imperative that means 'try doing (something) and see' or 'please look'. It is formed by adding ごらん (which comes from ごらんなさい, the polite command for 'look') to the て-form of a verb. The nuance is that you are inviting someone to attempt an action, often to see what happens or to experience something. It is softer than てみなさい and more casual than てみてください, but still carries a sense of instruction or suggestion from someone in a position of authority, like a parent, teacher, or older friend.