smart – smart is an adjective with two meanings 1) to talk about clothes - looking nice and neat 2) clever (the meaning in this video). “Learning English was a smart decision”.
to struggle – to have difficulty doing something “He struggled through the deep snow.”
the lot – all of something “I wanted some cake but my brother ate the lot.”
a fair share – a good, equal amount. “There was a lot of work but we all did our fair share.”
to lose your composure – to start to get upset or angry “She tried to stay calm but his unkind words made her lose her composure and she started to shout back at him.”
would sooner – an alternative to would rather “We can go to the party if you want but I’d sooner stay at home.”
to short-change someone – to not give enough money back “The beer was £4 and I gave the barman £10 but he short-changed me and only gave me £5 back!”
There is some other vocabulary which you maybe don't know but should be able to understand more or less from the context.
Here is the transcript if you want to check it later:
A pot of hazelnuts…and the flint that’s needed to open the lid. You need both to get a nut, but they’re separated by a see-through barrier. Vulcan has the rock but can’t reach the nuts. Virgil has the nuts but knows he can’t eat them without a rock.
Vulcan quickly offers the tool. He must hope Virgil is smart enough to open the lid and fair enough to cut him in on the spoils.
Virgil is struggling. He doesn’t have his friend’s skill and Vulcan is getting impatient. The flint is finally through the lid but can Virgil be trusted to share the nuts? With Vulcan out of reach it must be tempting to take the lot.
Three nuts - a fair share. Vulcan and Virgil have used teamwork to beat the system but can Capuchins really have a sense of fair-play?
Ted gives Vulcan a white chip which can be exchanged for food, in this case a dry biscuit. An identical token for Virgil but in return he gets a juicy grape - a far better exchange. Vigil is back for seconds, but this time Vulcan sees him get the grape, he now expects one too.
Biscuit? That’s not fair. Virgil is back again…another grape! Vulcan is losing his composure, this injustice is too much, he was happy with biscuit but that was before Virgil got grapes, now he’d sooner have nothing than be short-changed. It’s a point of principle.
Virgil returns, so Vulcan suspects Ted of readying another grape…must be in there somewhere. At last! – a succulent grape.