The verb wait is a dynamic verb which is also known as action verb or activity verb and it is opposite of stative verb.
One of the biggest differences between the Simple Present tense and Present Progressive (Continuous) for a dynamic verb is the former has a habitual aspect and the latter expresses incomplete action or state in progress at a specific time.
For example, let's contrast "I run" with "I am running". The former has a habitual (repetition) aspect and could be an answer to a question, "what kind of (physical) exercise do you do". "I run" means I run habitually to stay healthy. However, the latter means I am running now which is still in progress but we expect the action to finish soon and it could be an answer to "What are you doing (now)?". There is a huge difference.
Going back to your question, "I wait for your answer" can't express your progressive action you are performing at this moment. Nobody waits for an answer habitually or repeatedly. It happens only from time to time and doesn't happen on a regular basis. Therefore, it is more appropriate to use "I am waiting for your answer".
Present tense also has other aspects and it can mean a future action when you use the verbs like leave, start and depart, etc. For further information, please read the linked Wikipedia article.