Definition of Open Account Offer
What does the term "open account offer" mean in the world of sports betting? What is meant by an "open account offer"?

With the open account offers, the sports book will offer you a perk or two in exchange for signing up and depositing on the site.
A classic sign up offer would be a 100% deposit bonus of up to a certain amount. So, if you deposited $200 on the site initially, you would likely be eligible for a bonus of $200, which would be in the form of bet credits or something similar.
Another classic offer comes in the form of "free bets", which the sports books will allow you to use to place bets on outcomes that have certain minimum odds.
In the case of a "free bet", the sports books will usually let you keep the profits that the "free bets" generate.
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The sports betting world is extremely competitive, so you should always make sure to shop around before deciding which sports book to sign up and deposit at.