Just out of curiosity, is this a homework question? Feels kinda homeworky without a description.

Anyway, the conventions were a series of treaties, part of the later-named unequal treaties. They were not a single thing between a single pair of parties, but rather treaties involving the British, French and Russians, each pretty much independent of the others.

For the British, first, the Conventions gave Hong Kong to them. Prior to this it was simply leased. This ended the lease and made it permanent. This is not the thing that ended in 1997. Second, it leased the New Territories (Kowloon area) to the British. This was a lease, and it's this lease that was to end in 1997. Hong Kong proper wasn't intended to be returned initially, but when the UK returned the New Territories, the rest of HK was returned with it.

For Russia, the conventions gave them the land north of the Hēilóng/Amur River and east of the Wūsūlǐ/Ussuri River in Manchuria.

For the French, Tianjin was opened up as a treaty port. French ships were also permitted to transport Chinese labour, and France was paid additional indemnities by the Qing government.

It's not so much that amicable conditions were met so that the war could end. These are called the unequal treaties for a reason. The Qing was at a major disadvantage in this period, and the Conventions of Beijing were just a way to bring some closure, but at a high cost.