Abstractly, a vector is a direction and a length in some space. For example, in the space around you, a vector might be "from your face to your cup". There's multiple ways you can represent that vector with numbers. For example, it might be 1 foot forward, 1ft to the left, 1 ft down in the way you're facing, or it could be 1.4 ft north, 0ft east, 1ft down. Or even 45°left, 45°down, 1.7ft away. These are all equivalent descriptions of the same vector assuming you're facing northeast. In the space around you, you always need exactly three numbers to describe a vector, it's 3-dimensional. The numbers describe the vector, but the vector itself is just direction+length, no matter how you decide to put that into numbers.
Now there's other spaces that you can also use vectors in, that need a different number of numbers to describe. For example, the "what's the sportsball doing right this instant" is a 6-dimensional space: you need 3 numbers to describe where it is, and another 3 to describe in which direction and h