When the author writes that the Sykes-Picot Agreement "drew up" borders in the Middle East, they mean that it created new borders between the Middle Eastern lands which would be under French rule, and those which would be under British rule.
The idea was that in the context of the First World War, the Triple Entente (France, Great Britain and the Russian Empire) was more likely to win against the Ottoman Empire if its three members each had control over some regions in the Middle East. The secret agreement, signed in 1916, allocated the land as follows:
- Britain got part of Israel, Palestine, Jordan, Kuwait, and the southern part of Iraq,
- France got part of Turkey, the northern part of Iraq, Lebanon, and Syria,
- and Russia got Constantinople and part of Armenia.