(My answer is based on what I learned from the answer and comments of user 1muflon1. This answer wouldn't be possible without their patient attempts to put some knowledge under my thick skull. Here I will pretend to be another person and address Past-Me as "You").
At first, let's start with intuition for why increased consumption implies increased PPF. Then we will give more rigorous explanation if you won't be satisfied with said intuition.
Suppose we have a choice. We can either produce X of wine or produce Y of cheese and then trade Y of cheese for X of wine or produce Y of cheese and then use an alchemist to magically transform Y of cheese into X of wine. In all cases resulted wealth in terms of wine will be equal to X of wine. In the first case it's because 1 wine = 1 wine, in the second case it's because the exchange rate for Y cheese is equal to X of wine, in the third case because the transformation rate for Y cheese is equal to X of wine. Please note that even if we produce Y of cheese and then refuse to exchange/transform it the resulted wealth (i.e. Y of cheese) will still be worth X of wine. Just ability to perform exchange/transformation is enough for it to be X of wine. Consequently, if exchange/transformation rate will change, then so will worth of our wealth in terms of wine.
Now suppose we can hire a more experienced alchemist (who knows more advanced and nuanced alchemy) to replace our current alchemist. This new alchemist can transform Y of cheese in Z of wine, where Z>X. What will happen if we hire them? It would mean that transformation rate for our cheese production improved, meaning that by producing Y of cheese we now produce more in terms of wine, that now we have better alchemist technology. As a consequence, it would mean that our our PPF increased.
Now suppose that we have our not very good old achemist, but we have a possibility to improve our exchange rate for Y of cheese. Suppose our current exchange rate is based on our internal (i.e. national) market and we are an autarky. But in the external world there is a country that can give us a better bargain for our cheese, let's call it Winetopia. If trade negotiations with Winetopia will be successfull then it will agree to exchange Y of our cheese for Z of its wine, where Z>X. Thus after we negotiate terms of trade with Winetopia value of our Y of cheese in terms in wine will increase. We still produce only Y of cheese, but now Y of cheese represents more wealth in terms of wine thanks for better exchange rate. As we saw in the example above, we could have the same increase in wealth if we hired a better alchemist. In the example with a better alchemist we concluded that use of a better alchemist leads to increased PPF. This example with Winetopia has no significant difference with the above alchemical example, thus by analogy we can make similiar conclusion, namely that improved exchange rate leads to increased PPF.
If you don't like this explanation, then we can take the alternative approach:
GDP measures production, if real GDP (nominal GDP isn't enough because its changes can be attributed to deflation/inflation) increased after trade (assuming that before trade stared we already were on PPF, rather than below it) with Winetopia then our PPF increased too.
For this we first have to put some numbers on the problem to be able to draw PPFs and consumption curves. Lets assume that Cheestopia can produce 1 cheese at 1 labor, and 1 wine at 2 labor and Winetopia 1 cheese at 2 labor and 1 wine at 1 labor, and both countries have 100 labor avaiable for production, this gives us the following PPFs for both countries in autarky(the chart was created by 1muflon1):
Production and consumption curves are equal here (for now) because everything produced domestically is consumed domestically and everything consumed domestically was produced domestically. Cheesetopia has the comparative advantage at producing cheese, while Winetopia has the comparative advantage at producing wine. For this particular example let's suppose that Cheesetopia doesn't value cheese at all, but values wine, while Winetopia doesn't value wine at all, but values cheese. Thus Cheesetopia spends all its labor to produce 50 wine, while Winetopia spends all its labor to produce 50 cheese. From given information we will be able to deduce/calculate following table:
Numbers in yellow cells (except of price of 1 cheese in terms of cheese, which is obviously always 1 cheese under any circumstances) were calculated based on numbers in white cells. Theoretically it's possible to calculate price of 1 wine in terms of cheese from data that we already have, but here I will just take word of user 1muflon1 that said prices are correct and omit calculations. Calculations for the table themselves are based on what was described in comments by 1muflon1 here(It starts with words "repeating itself"):Do I make correct conclusions about international trade (and ways to increase GDP) from the expedenture approach formula for GDP? As for nominal GDP of Cheesetopia (we don't count GDP for Winetopia because it's excessive for our purposes), it's GDP=100 before trade(C=100, everything else equals zero) and GDP=100+50-50 (C=100, X=50, M=50) after trade. In all cases GDP is shown in terms of cheese. Thus we see why both nominal GDP for Cheseetopia before trade (i.e. "Cheesetopia Old") and nominal GDP for Cheesetopia after trade (i.e."Cheesetopia New") are equal to 100. The table shows real GDP of Cheesetopia increased after trade, thus we can conclude that its PPF increased after trade. Its PPF now ends in point (0ch,100w) instead of old point (0ch,50w).
One more thing. A sceptic could try to provide the alternative explanation: "Post-trade production in terms of cheese increased NOT due to trade, but because Cheesetopia now spends all its labor on producing the good of its comparative advantage, namely cheese". But they would be wrong.Production in terms of cheese will never increase just due to specialization. Because no matter if we specialize or not, we are still on the same PPF, thus real GDP will be the same anyway.