Thank you for your question. Patience is a wise and effective strategy in dealing with problems both in terms of their consequences in this world as well as the consequences in the next. As for this world, patience stops problems from becoming more exasperated, as when a person is not patient they become anxious and worried and that means that the problem becomes internal as well as external. At times, being patient in a situation can defuse the problem itself or at least limit it from spiralling out of control.
As for its effects on the personal development of a person, tests and trials are a means through which Allah increases the belief of His servants and in some traditions, it is mentioned that when a person cannot reach a level through their own actions and worship, Allah sends a test for them to be patient through so that He can raise them to those levels that they could not attain themselves. Patience also carries great rewards in the hereafter in relation to the difficulty of the test.
For more explanation on this issue please refer to this three-part series of The Scale of Wisdom Podcast:
Particularly useful for this discussion are the episodes on faith and anxiety as well.
May you always be successful.