Responses to forum questions travel through a process of suggesting and accepting answers in order to arrive at what is the ultimate goal: getting the author a sound and satisfactory response to their question.
Suggested Answers
When answering a question, you can click suggest as answer to indicate your confidence in the accuracy of your response. This functionality exists on the first response as well as any of the later responses to the thread. 
Suggested answers are highlighted within the thread and the author of the question (as well as anyone else who had the question) will be notified that a potential answer has been provided. The author and others who shared the question can then review the answer and, possibly, accept it.
Accepted Answers
Any reply (suggested or otherwise) can be accepted as an answer by the author of the question and anyone who clicks I have this question too. When you, as author, mark an answer as accepted, you are essentially letting the answerer know the value of their response, and communicating that you are satisfied with the answer to the original question. 
The threshold for accepting an answer is different for the author of the question and for those users who clicked I have this question too. If you are the author of the question, you can accept in one click. If you indicated that I have this question too, you will see the accept option. However, the question needs to be accepted by at least two users who also had the question in order to appear as accepted.
Any member can vote an answer up to improve the answer's visibility on the site. However, voting up has no bearing on acceptance.
Rejected Answers
The author of the question (and anyone who also had the question) can also reject answers by clicking reject answer below the response. This simply indicates that the answer is not satisfactory and invites others to offer alternative responses.