In Japanese, talking about family members is more complicated than in English. This is mainly due to the fact that there are different words for mother, father, sister, etc., depending on whether you're referring to your own family member or someone else's.
So, for example, if I was referring to my own mother in conversation I would use 母, but if I was talking about someone else's mother, I would refer to her as お母さん.
It is important to note that this rule applies only when speaking with a non-family member. It is perfectly natural to call one's own mother お母さん when addressing her directly. You can think of it this way: just as you do not use the polite suffix -さん when talking about yourself, neither do you use the polite form when speaking about your own family.
Another point worth noting is that when referring to your family members with the plain form, you do not need to use 私の(my) or 私たちの(our), as this would be redundant.
Below is a list of the different family words in both their plain and polite forms. Some words, however, do not have a different plain and polite form. For these words, simply use the suffix -さん when talking about someone else's family.
The ご that you see in ご両親 is an honorific similar to お in for example お店. The difference is that お is used in front of words that use an originally Japanese, or 訓読み pronuncation, whereas ご is used in front of words that use pronunciations that are derived from Chinese, called 音読み.