У меня - I have У тебя - You have У него - He has У неё - She has У нас - We have У вас - They have У них - They have
У вас is said to a group of people who you are talking more directly, у них is said to a person/people when you are talking about someone else, for example you say to your teacher pointing at a group of students 'They have it'
It is indeed, but it's caused by the fact that in Russian you go formal by using plural forms of pronouns that refer to the person you are talking to. For example, "ty" is the proper translation of "you" when you're talking to a colleague, but you should use the plural form "vy" when talking to an adult stranger or somebody who's somehow superior to you.
This manner of switching to formal speech by the use of plural pronouns is not limited to Russian. Here's an article on how it's done in various languages:
Just to note something. Think it is important. In the old days, back here in my country (Serbia) we used to talk like that. Instead of: Ја имам which lierally means I have, we used to say У мене, which meant the same thing like in Russian. It is a less agressive way to say that you HAVE something. It was used with family, friends, even domestic animals, due to respect, but not for things, such as house. Today we use only more agressive way of expressing possession, but Russians kept it in the more broader sense. So when they say У меня есть, that goes for everything. I only wanted to emphasize that У меня есть is a way of expression possession in a more milder way. And it literally means "Inside me".
Mightypotatoes states that у меня is used in that sentence as "by me"; As I understand, у is not referring to I, nor in any way English speakers normally use subjects (menya nor tebya are subjects); rather it indicates possession. Such an example is У тебя есть кошка, where is refers to "By you is a cat" whereas У меня есть кошка is "By me is a cat". The cat here is actually the subject, which is "being". Hope I was helpful.