Laser mode locking

Having read Madan Ivan's (nice) answer and the comments that follow it seems that your confusion stems from your assumption that the many standing modes are already in phase with one another. You said in a comment above that "only by boundary conditions there will have a place where sin are in phase", but the boundary conditions only dictate which modes can exist in the cavity, and do not have any implications on the relative phase of each of the cavity modes. Your statement is therefore technically wrong, and I think that this is what is causing the confusion. Each of the modes can exist in the cavity with a phase which is independent of all of the other modes, and thus a laser which is free-running with N modes of equal amplitude will produce noise, and not a highly ordered pulse train.

When modelocking a cavity, some nonlinearity (either 'passively' or 'actively' introduced) is required in order to establish a well defined phase relationship between each of the modes which is then reproduced each roundtrip, as is demonstrated by your nice graphic (i.e., the modes of the cavity are phase locked, hence "modelocking"). This then allows for the pulsed output.

You also asked why one mode will become dominant over another when modelocking is not used. This is simply because the net roundtrip loss for one particular mode is less, allowing it to build up and reach steady-state before the others. Once this occurs this mode will dominate the cavity and take the lion's share of stored energy, thus keeping all other modes suppressed. (Edit in light of a more recent comment: This can occur in such a way that a few modes can co-exist in the cavity if the gain and cavity loss profiles allow them to. However, the argument above still holds when considering the number of modes present in a modelocked pulse - $\sim 10^{6}$ - in comparison with a free-running cavity which allows for a few modes at any given time).

In order to stop this from happening and to cause a cavity to modelock, you need to set the cavity up in such a way that loss is reduced for high intensities, which are provided when the standing modes of the cavity are in phase. If this is done correctly, then the most stable operating point for the cavity will be the modelocked state, and not the single-longitudinal-mode state which would otherwise dominate.