What's normal? Well it ain't me I'll tell you that right now :P
Partly for what Alkeni said, I also have asperger's but mine got to the point where the only person to ever find out (who I or someone else didn't tell) was someone who himself had aspergers. My lack of being normal also just has to do with... I don't get along with most people, I don't relate to them, I don't understand them, my interests are no where close to there's. Or maybe that's just the kind of normal I've been exposed to. In my area most people just want to chill, have fun, go home, sleep, have fun again. Whenever anything somewhat complicated comes up (moral questions, debates, interest in a science or technology) etc. they not only try to avoid it like the plague but somehow snap and get mad as if the people who do enjoy these things are assholes for taking the time to expand their mind rather than simply looking to chill out with others everyday.
Now, what actually makes normal though? I say it varies culture to culture, but it's basically the most typical/average mentality, interests and behaviour of the culture and area. And usually this becomes the culturally accepted way of acting/behaving simply because it's what most people understand, identify and relate to. Some culture's may embrace being different and not be afraid or hide from people not normal but rather embrace them, but there are also many cultures who see people outside the norm was something scary, weird, threatening and something to be afraid of and vicious towards.
And it seems the topic of High School also came up so I'll address this as well.
High School is an exception, but at the same time the avatar to the rule of culture and being normal.
Human's are naturally curious but also social and fearful creatures. They seek to be accepted to matter what, and they are afraid of what they don't understand.
Hell look at any religious war, crusade, witch burning or simply paranoia/fear of things like D&D is demon worshiping, video games make murderers etc for examples of this.
They find a group, they stick with the group and become vicious to the rest in both fear and an attempt to reach the top of the power scale.
You've got the normies, those who subscribe to the culturally accepted behaviour and are the majority. Nothing too special, nothing too interesting, they just make the bulk of the community.
Then you got the popular people, those who are close enough to normal people that they are accepted and like, but also possess characteristics that they do not possess (or not as strongly) which puts them above the others.
Typically in High School with them being teenager's they value things like attractiveness, sports, sex, and anything that's simply fun and requires little thinking to be more relatable and valued. So you get the people who love to party, do sports, be cheerleaders and then fuck all night long on top.
Then you got the unpopular people, those who may either simply not subscribe to the normal culture, or those who possess characteristics they do not like. In High School sense this is normally something such as Intelligence or Maturity (It either Intimidates them or inconveniences their ability to simply relax), a skill that gains them more recognition/praise from adults and others that leads to the jelliousy of the other kids (High grades, good with computers), or simply a hobby/interest that most people don't subscribe to and find as weird (Warhammer, Magic, D&D).
The general rule of thumb still applies outside of high school, but what becomes valued changes.
Suddenly in the working and post-secondary education world, Intelligence, Advanced skills, maturity etc becomes the most valued charactertistics (Normally because this leads to better jobs, more renown, more money and power etc.) and suddenly High School's whole culture turns upside down. Those who were normally picked on for their skills and mindset become valued and on top, and those who were valued for simply throwing a ball and acting tough find themselves with not as many tools, so their popularity takes a hit.
Ok, that went on longer than I meant for it too... :/
TLDR: Normal is the most common/typical behaviour and mindset in the community.
Subscribing to this makes you normal, relating to this but having something different that said culture values makes you more popular.
Not subscribing or having skills either unvalued or seen as fearful/intimidating makes you unpopular.