"I have a computer."
Translation:Nekem van számítógépem.
It would put the emphasis on "számítógép" (computer), meaning that you have a computer, and not someting else. For example, "Nekem számítógépem van, nem rádióm."="I have a computer, and not a radio."
ok, but many sentences here are built like this (with the van in the end), without a second sentence
In Hungarian the word order is generally free. This means that especially for basic sentences, every, or almost every possible order is correct. The thing is, that they all differ in their meanings, usually in the emphasised word. Therefore I can't say that any of the sentences you've met are wrong, but they might be rare sentences only used in special situations.
You do not necessarily need a second sentence. You could be sitting in a classroom where the teacher asks everybody to say what they have.
Nekem kutyám van. - I have a dog.
Nekem biciklim van. - I have a bicycle.
Nekem számítógépem van. - I have a computer.
All these are emphasizing the thing/object. Because that is what was placed in front of the verb.