Practical matter of the Higgs-Mechanism My maybe very naive question is, of what practical importance will the discovery of the Higgs-Mechanism be for our technological advance in the near future?
 A: I don't think that's a naive question at all, as there's quite a lot to it.
The immediate answer is "no difference". If you, like many of us, read science fiction as an impressionable youngster you're probably vaguely disappointed that warp engines and interdimensional drives haven't been invented yet, and you probably harbour hopes that some new discovery could still make them possible.
The problem is that the Standard Model is an extremely accurate description of the world at low energies. There are undoubtably new discoveries to come, but by definition they'll be at high energies that we don't see in the world around us. This probably means the technologies we'll invent have to be based on Standard Model physics. Any new discoverties aren't likely to have a big impact on technology. I say "probably" because I'm keenly aware of Arthur C. Clarke's first law and it would be a brave man to claim discoveries like the Higgs will never affect everyday technology.
However, discovering the Higgs has required enormous advances in areas like computing, and this is likely to have a big effect on all of us in the near future, especially if cloud computing takes off. After all, remember that the World Wide Web was invented at Cern.
A: People tend to talk about the role of the Higg's in particle mass, but this is in some sense a peripheral issue to something much deeper. This deeper issue is that without the Higgs, W boson scattering violates unitarity above $\sim 1000 \text{ GeV}$, or equivalently the Standard Model minus the Higgs is non-renormalizable above  $\sim 1000 \text{ GeV}$. 
Now to break down some of these buzzwords: This deeper issue I speak of is due to the fact that when we do calculations in particle physics we are using quantum mechanics which is an intrinsically probabilistic theory. In such a theory we don't have classical notions of trajectory etc, and all we can calculate is the probability that some process is going to occur. For example, a typically thing we might be interested in is the probability that some particle will be scattering off at some angle with some energy. Note that this is not a deficiency of the theory that we are limited to probabilistic predictions since as far as we know there is no meta theory that will ever be able to use to predict how a single given particle will behave. Now, since we are dealing with probabilities we should never calculate a probablity that is more than %100 or else the theory we are dealing with ceases to make sense. This is exactly what I mean by ' violates unitarity' - the Standard Model minus the Higgs makes no sense above $\sim 1000 \text{ GeV}$ as it starts giving nonsensical probabilities in this regime. With the Higgs however it is a logically complete theory to much higher energies (perhaps arbitrarily large ) in that the probabilities always come out bounded by 100%. It may not (probably won't) be the correct theory that describes our world up to arbitrarily large energies, but it is at least mathematically consistent, which is more than you can say for the Standard model without the Higgs. 
So to summarize and answer your question: now that we know (pretty sure) there is a Higgs we can make predictions using the Standard Model to higher energies than if we didn't see a Higgs. Any deviations between experiment and theory will now be a sign of new physics instead of an artifact of our theory logically breaking down. 
If you want a deeper explanation in either laymans terms or physics terms let me know. 
