Patience is a great way to show and gain respect. The more you get to know somebody and how they work the more respect there will be. If you rush your judgement, you could make the wrong assumption about somebody.
It is also a great way to improve productivity and quality. Rushing to get something done does nothing but induce stress and produce work that is inferior in quality. Practising patience allows you to properly work on your given task because you're not trying to just get the job done, you're actually focusing on producing good work.
In the workplace there will be testing times and your ability to be patient can tip the scale in a positive direction. Being patient and trying to understand and diffuse a situation allows everyone to work in a harmonious environment.
You will at one point or another have to team up with a colleague to get something done. If you have no patience in dealing with people, whether someone who works fast or slow, you will create an environment where teamwork suffers. Being patient allows you to understand that different people work in different paces and are still able to produce great work, creating an environment that promotes building strong bonds and relationships.
There will be times where people push your buttons a little too far and you feel your patience reducing, it is especially important to put into practise this skill in those moments. It is better to be patient than to have an outburst.
Show and gain respect
Improves productivity and quality
Diffuses a tense situation
Builds stronger bonds and relationships