Tension music is to do just that, create tension, add drama and add suspense.
As stated before the quick cuts are used to create suspense and also get the audiences heart racing.
Here are some conventions of a thriller movie (not all of them are included and there can be others swell depending on the storyline of the film).
This helps add drama and suspense to the film/scene. It adds a certain atmosphere that the film makers want to get across to the audience.
This could be towards a enemy, within groups or on a larger scale for example war.
With thiller movies it is mainly between two individuals or groups.
These are used to show flashbacks and add suspense.
This is to create suspense and is normally used accompanied by silence to add maximum tension.