Advance ticket for travel in U.K.

I just found an outstanding price for a Saturday train from Edinburgh to York, but the fine print says "..... The Advance ticket does not have guaranteed availability. Early booking is recommended. Availability: Tickets must be purchased in advance and is not available for purchase on the day of travel. This ticket is not guaranteed on any train and availability may be limited."

This is on a British XC train for April, but the fine print makes me wonder that if even if I have a ticket, I may not be guaranteed travel. Confused! Mary
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