Converge

As one can tell by its shape, converging leads to ‘less solutions’, less choices. In designer’s language: the solution space is defined further.
For example, if one is to move a pile of wood and 8 solutions are invented, choosing a wheelbarrow refines the space of solutions. From now on, everybody focusses on wheelbarrows. Converging is necessary to keep the project from floating around without advancing.
With the yellow sticky notes, one can define the way choices are made. It is important that there is some method used for this, otherwise the dominant team members will simply decide. Usually, the decision process becomes more elaborate and rational further in the project, when solutions become more concrete. So, dot voting is usually good enough for ideas, while concepts are for example scored on the product requirements list.

What if I don’t converge?

You won’t make much progress. If you don’t make rational choices, but just choose using your (or the groups) gut feeling, you might end up designing something that does not comply with the budget.

Where in the design flow?

Usually at least after diverging.

Which method to use?

Depends mainly on the elaboration level of the solutions. The more concrete a solution, the better it’s properties can be estimated to the requirements.