I was reading about wake models. However it is unclear to me how they are used to model wind turbines. Could anybody explain me what are wake models and why it is important to predict wakes in wind turbines?

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The second slide of the presentation linked by you actually shows the issue with wake very clearly. You could also talk about turbulences instead of wake (my company actually does). Wake is simply the pertubation of the flow of the wind by wind turbines (or any other object, like hills, trees, buildings, airplane noses, the grill on the new SUV by Chrysler, etc). This pertubation can be modelled (please don't ask what the formulas are, I miserably failed that course in university).

So why is the prediction important? The first turbines in the direction of the oncoming wind are able to produce (slightly) more energy since the wind is streaming rather undisturbed. The second row of turbines can take less energy from the wind, since it was already slowed down and pertubed a bit by the first row. The same goes for any other turbines standing further back. So you need to know, how the wake most likely is shaped, considering topography and placement of turbines, in order to maximise the yield of you wind park.

Also, wake, or turbulences, can put stress on materials. Anyone who ever flew on a plane knows how turbulences can feel. Now imagine you expose an airplane wing to rather heavy turbulences all day round (okay, sometimes there are lulls) for 20 years. The material is put under a lot of strain, and sometimes it may break. Also the vibrations of the turbulences may affect the generator. So wake models also reduce the possibility of (near) total loss on a wind turbine.

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