Like yeast itself, this is a very simple question yet when we look into it there is actually a lot of complexity if you wish to look deeper. But first I will begin with the basic points
Yeast are a type of fungus.
They are a single celled organism.
Yeast break down carbohydrate into smaller stuff, for us this means breaking down sugars into alcohol and other substances.
Not everything produced is wanted though, this includes by-products such as carbon dioxide and proteins.
They reproduce asexual and with enough carbohydrates to survive yeast still keep growing in number.
Yeast generally does not want to be subject to high temperatures as it will die, though certain strains can survive past 100C brewing yeast wants to be less than 30-40C.
At very cool temperatures yeast will become inactive.
These are the basics you need to know for what yeast is doing in your brew, but there is more to it than that. One important point is that there are many strains of yeast which will have different effects.
Any easy one to notice difference for brewers is between Ale and Lager yeast. Ale yeast ferments on the top, while Lager yeast ferments on the bottom. But there is more going on than that. Both types create some different enzymes, these are small proteins which will help break down the carbohydrates differently. This only gets more complex when we look into different types of Ale and Lager yeast which helps give us variety in flavour.
This also applies to other types of yeasts. Many older brewers will be familiar with using baker’s yeast which would give off a bready taste much of the time. Well that is simply because that yeast breaks down the ingredients to create a flavour we know from bread.
Wild yeasts are also an important subject, though for many problem is more accurate. The reason we have developed specific types of yeast is to get a consistently good flavour being produced, at least if everything else goes right. With wild yeasts you add a certain random element, it can turn out well and many love experimenting with them but a lot of the time they simply can spoil a brew. This is why it is very important to make sure any ingredients you use have been cleaned as has any equipment, you never know when a particularly resilient strain has crept in. If you do get some in a brew you have to make sure any equipment, especially plastic, is cleaned thoroughly as it can be especially hard to get rid of. Soaking in a cleaning solution is a good bet.
There is much more too yeast than this, but that is where it starts to get more technical which can help you with brewing but is not necessary to do so.