I'm new to D&D and trying to create a character to play with. I'm a bit confused by the skills. My character is a bard with the entertainer background. The bard class gives me three skills of my choice, and the entertainer background gives me proficiency in acrobatics and performance. Does this mean I have 3 skills of my choice, plus acrobatics and performance? Or does this mean I have three skills of my choice and if I choose acrobatics and performance then I get proficiency in those two skills?
"Having" a skill in 5e is "proficient in" said skill.
Skills are boolean - either you're proficient (and add your Proficiency Bonus and the attribute modifier to the rolls) or not (in which case you still get to add the attribute modifier).
So, since you took the entertainer background, yes, you "have" those two skills, acrobatics and performance.
The Bard class doesn't specify which skills, so any not granted by race or background are fair game to pick. Three more skills, you pick, become proficient.
So you should "have" a total of five proficient skills. The other skills all are non-proficient (at least until you get Jack of All Trades feature).
Bards' Jack of All Trades makes unskilled rolls half-proficient - half your proficiency mod is used unless you're proficient.
And one other thing: If background and class give the same skill, you can pick any other skill instead for the overlap.
You have proficiency in all of the skills your background gives you, plus all of the skills your class gives you.
Having proficiency in the skill and "getting" the skill mean the same thing. In both cases, it means you get to add your proficiency bonus (which as a 1st level character is +2) to d20 rolls made with that skill, in addition to the ability modifier associated with that skill.