Paraphrase:

a car registered and insured in New York with driver and passengers resident and domiciled in New York, leaves the road in Ontario during an over-the-border drive. One of the passengers is injured and sues the driver for recompense, the court applied the law of New York, because it was plainly the legal system with which these facts had their closest connection, contained no such limitation and, if applied would allow Miss Babcock, the injured passenger to recover.

A car from New York, with New York residents as the driver and passengers, had an accident in Ontario. One passenger was injured and sued the driver for compensation. The court decided to use the laws of New York in the case, as they were most closely related to the situation and did not have any restrictions that would prevent the injured passenger from receiving compensation.