To check something out is to examine it closely or look at it carefully.
Example: You should check out our list of common expressions.
For more meanings of the phrasal verb check out
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To start afresh is to begin again, often with the sense of making a break with the past.
Example: I want to move to a new city and start afresh.
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Here one is being used instead of you as the pronoun for an indefinite person. Using one like this is quite formal-sounding.
One is not amused.