What this film is about, what it means (HERE BE SPOILERS)
First of all, let me say that I don't really like this film that much, there is some poor editing and there are some scenes that could have been done away with. I do like however some of the long scenes (or 'longeurs') where we see a car drive away.
OK. Back to the movie. Katia is speaking French in the movie but SHE IS NOT PLAYING A FRENCH GIRL. This is something that many of the people on this comments board appear to have misunderstood, perhaps because they do not speak French themselves. (This, therefore, is a flaw in the direction, as clearly it is not made clear enough for non-French speakers).
She is Russian. She actually speaks Russian some of the time (which is when David gets frustrated with her and asks her to speak in French). She also clearly is hiding a big secret which we can't fathom out. But there's something clearly wrong with her, and David wants to connect with Katia but this secret is holding back their relationship. She keeps saying things that don't make sense, contradicting herself -- such as when he jokes whether he should shave his hair like the marine at the ice-cream parlour, she says she doesn't like shaved hair and then she says she does. This confuses him. It's only later when this becomes relevant. So the only time they can "connect" is during sexual intercourse. The rest of the time is tense, to say the least. David tries to make the best of things because he really doesn't want to lose her, but cannot make her tell him this big secret/problem. But he perserveres.
At one point he gets fed up with her and throws her out of the motel room. While she's out she sees a car that worries her. David then gets worried, goes out to look for her, and at one point she freaks out when she sees a white car (not necessarily the same car she's worried about). David gets even more frustrated as he knows this is something to do with the big secret/problem but cannot slap it out of her.
They drive off again, and at one point they climb this really hard to get to hill. Actually, she is driving at this point. Could it be that she wanted to get a vantage point, to see if she could see the car coming? At one point they get out and she is looking out over the distance. He then looks at where she was looking -- a path, probably the path they should have stayed on. Again, he knows instinctively that she is worried about who could be following them. He decides to take over the wheel. More tension between them.
Anyhow, shortly after that they are back on a straight road, when the horrible rape scene happens. Their car gets rammed off the road, the three heavies get out, I assume they are from Katia's home-country -- Russia -- but they don't talk so who knows. Whatever it is, they are here to teach Katia some kind of lesson. So they take them both out of the car, strip her (but do nothing else to her) and instead her boyfriend gets beaten to a pulp and raped in front of her. One of the guys holds her to force her to watch. They leave, without putting a finger on her again. This was their revenge. And from the look in her eyes, this is possibly something that has happened to previous boyfriends in the past. (In fact, I'd say almost certainly, which is why she acts so weirdly). Who were these guys? Some kind of Russian mafia mob perhaps, but I would like to think that the bald guy is actually her ex, and this is his revenge for something that she did to him -- probably was unfaithful -- by tracking down all her subsequent relationships and taking similar revenge each time. Interestingly, he is shaven-headed, which may explain why she was so confused back in the ice-cream parlour, as it reminded her of her ex.
Back in the hotel, well David goes crazy and stabs her to death which is a very shocking scene. We would have to assume he's put two and two together... remembered her panic when she saw a white car earlier, her inability to tell him what the problem was, the fact that it was him and not her who got attacked etc. So he does what he does. Perhaps because of the trauma he has been through, perhaps because he is brain damaged somewhat from being beaten over the head repeatedly with a bat, or perhaps because he realises that otherwise this is going to happen to some other poor future boyfriend.... -- this latter reason is the one that the arthouse-lover in me prefers.. Interestingly, he shaves his head first, perhaps to show that he now realises why she was so confused earlier when he was joking about the marine -- her ex also had the same haircut. He then drives into the desert and kills himself. Nothing left to live for, he's seriously disfigured and is now a murderer. In the end, the desolation of his situation is further emphasised by the conversation of the cop over the two-way phone, who is trying to get his colleague to send over backup so that they can block the roads to prevent a schoolbus from seeing the naked David, but the only other car available is busy dealing with a DUI, which the cop cannot believe is more urgent. There's no mention of the body in the hotel yet, it probably has yet to be found. Another problem with the film is that the cop's radio conversation is far too quiet, bad sound mixing here.
Anyhow, so that's how I saw it. If you think I'm reading too much into it then so be it. I don't really like this film, but I certainly do not think it is worthy of the negative comments here on this board, it's actually quite a deep and meaningful movie, you just have to think about it a little more. The strange ending happens for a reason, to say "What a ridiculous ending" without trying to work out what it was about is a very shallow way to look at arthouse cinema.
But do I recommend this film? Not particularly. It could have been a lot, lot better!
ONE FINAL POINT
All the stuff above is one way of looking at the film. It's plausible, it explains why what happened happened, and there are hints about this (the white car, etc) throughout the movie. You may have another take on it. And the beauty is, because of the ambiguity, you may be right. In fact, anyone can have their own take on it as not everything is spelled out. That's why I love European-style cinema, and I really don't like film where one's hand is held throughout and it all makes sense in the end. It means you don't really have to think much for yourself. Leaving it rather vague means that you get to have a real think after you've seen a movie, and come up with your own reasons for why what happens, happens. In fact, the irony is that the character we can most identify with in the whole movie is the cop at the end, who now has the job to try and work out what the hell has just happened. My take above is not wrong, but it's as good as any other person's take on what happened, given the information we are given. Like David, and now the cop, we too are left very much in the dark!