What does he mean when he says don't get too attached?

It means that he is seriously not sure about you and don't be upset of surprised if one day he just says he doesn't want to go out with you anymore.  He's preparing your mind for disappointment, because guys don't really want to upset women.

So I've been with my boyfriend for about 6 months

Oh six months, you could add he doesn't want too much committment to the above paragraph as well. So don't go thinking he's going to get engaged or married to you anytime soon.

and things are going well. We get on really well, don't argue very often and in general,

Just because you don't argue, it doesn't mean things are going brilliantly.  It could just mean that you are both hiding the fact you are annoyed with certain things, in order not to cause an argument.

we just have a good time together. I'm unsure, however, as to where exactly this is all going.

His first relationship lasted 2 and a half years. They broke up last February and had been living together for a year before he moved to another city for university. He admitted that she broke his heart and from the general gist, she broke up with him because he had changed (he didn't go into this) and he wasn't a good boyfriend and didn't contact her enough.

That is probably the route of the problem then, he's probably not moved on from her and is basically in a relationship with you not knowing whether he likes you enough, because he's still dwelling on that relationship.  He could also want to avoid the hurt of the last relationship by testing out how interested you are.  This other ex-girlfriend obviously wasn't that interested in him, so maybe he's testing out how interested you are, to make sure you are not going to do a runner on him as well.

So I get he's not over her yet - that's fine. But then a few weeks ago, he told me that he liked the way things were and he liked that we weren't too serious.

He probably got serious with her and now he's frightened of getting serious with any other woman, in case she does a runner and hurts him again. He wants to move seriously slowly.

What on earth does that mean? He's away at the momentt so last night, I texted him telling him that I missed his teasing (he teases me a LOT). His reply was: do you miss the teasing or are you getting attached or something?

Oh, no, that isn't good, that's the sign of a guy that's in a relationship simply because he doesn't want to be single, but not wanting a woman that's high maintenance at the same time.

Neither of us have siad the 'love' word yet.

Well it has to be said only if it's true and if it doesn't feel right saying it, it shouldn't be said.

I think I am falling in love with him but from what he's saying to me, it seems that my feelings aren't being reciprocated.

He certainly isn't at the same level as you.  I think as I say he maybe in the relationship simply because he doesn't want to be single.  6 months is a long time to last in a relationship, if you feel it's not working out, but maybe he's waiting for someone better to come along while he's with you, then he can move from one relationship into the next.

He said to me before that he was afraid that I would break his heart so I do understand his caution to a certain extent but is he pretty much telling me that he will never have a serious relationship with me?

That's what you need to discuss with him, find out the truth.  Yes, from what you say about his last relationship he will be worried about that.  But you need to find out the truth so you can decide whether to move on or not.  It may cause an argument, but the other option is you are not going to know where you stand with him, so things will be building up towards a split up.  It's better to try and find out the truth and possibly go through an argument in this situation.

What I don't get is that he is nearly bipolar in his attitude to our relationship: at times, he says we're not too serious and he doesn't want me getting attached yet he wonders why I haven't introduced him to my parents

The fact that you haven't introduced him to your parents will make him insecure and he will want to pretend that he doesn't want to get serious, in order to protect himself from the hurt should you decide to ditch him.

and after only a few weeks together, he told me I would make a great mother.

Some guys will tell women things that they want to hear, but saying those specific words about being a great mother, is more likely to be something that he's been thinking about.  And he does think you'd make a great mother, so he's assessing your abilities.

I'm just really confused as to where this is all going.

I think you need to get your answers out of him.  Ask him are you insecure because of your last relationship or are you genuinely not wanting to get serious with me.

I would whatever it is that's bothering him is to do with not being over his last relationship.  He's not been able to move on yet and forget about it and is therefore carrying it over into your relationship. I think the most likely option is he is insecure but there's also the possibility that he might not be too interested in you and is just in a relationship to make him feel better and wanted and desired by a woman.