So i sent a jpg to graphic designer to have some hoodies silk screened... I send a jpg of the image.... I some wacky graphic back that looks like garbage, i say use what I gave you, and they say... We need a vector.... so I used some online conversion site and converted my bmp to a eps file.... So is that a vector? Did I do what they needed or not?

Probably not and if it did get vectorized, it's most likely a bad job of one
What you sent them is a raster image which is made out of pixels, if they need to scale it up or down to fit the hoodies, the pixels will get stretched and distorted
Vector images are made out of shapes and don't distort when scaled up or down, it would be better if you posted a request to have someone do it for you or pay someone to do it elsewhere
Be prepared to pay a lot though, as vectoring is very time consuming, especially if your image is very detailed and/or complex

yah like agonist said. it depends how simple/detailed you want the vector image to be. There are ways you can convert a image into vector with certain programs

looking through it