The Subscription is a form of purchase agreement that differentiates itself from the classic purchase and sale agreement of securities, because it creates said securities through its execution. Except for this essential differentiation, it is a normal purchase and sale agreement.
Unilateral and then Bilateral
In common law, a subscription agreement begins generally by being a unilateral application by an investor to buy a certain number of shares of stock of an issuing company at a certain price stated by an offering memorandum describing a private issue.
The board of directors of the issuing company reviews the each subscription to approve or reject it. If the subscription is approved, the board of directors determines whether it is fully or partially executed, in other words how many shares of stock will be sold to the investor on that specific subscription.
As soon as the subscription is approved, whether totally or partially, the subscription agreement becomes bilateral.
Beware of Polysemy!
The term of subscription also refers also to another agreement where a customer must pay a periodical subscription price to have access to a product or service. That kind of subscription was pioneered by magazines and newspapers and is now used by many businesses and websites, but it has nothing to do with the securities world.