first boyfriend

I met my first boyfriend, my first real boyfriend, in my hometown.

A 'boyfriend' is a male that you have a romantic relationship with.  A 'first boyfriend' is the initial boyfriend that you have.  Notice the following:

1. I met my first boyfriend at a cafe.
   
2. How long were you with your first boyfriend?
   

crush

I had a crush on him when I was younger.

When we romantically like someone, often in a simple way when we're young, then we have a 'crush' on them. Notice the following:

1. I don't understand why you have a crush on him.
   
2. I have had a crush on him since elementary school.
   

carry on

We met at a club one night and we carried on from there.

To 'carry on' is to continue doing something, in this case they continued the relationship from there.  Notice the following:

1. Why do we have to carry on with this conversation?
   
2. Everyone else was tired but I wanted to carry on with the night.
   

stubble

I don't know why I like short beards; I like stubble.

'Stubble' is very short hair on the face that is rough if you touch it.  Notice the following:

1. He always has a little bit of stubble on his face.
   
2. You need to shave before work. You have stubble.
   

serious relationship

We're still young, but we have a serious relationship.

A 'serious relationship' is one that has a possible future in marriage, it is not just dating casually or for fun.  Notice the following:

1. He isn't ready for a serious relationship right now.
   
2. They were in a serious relationship all through college.