if an object has a fill AND stroke, & you want to convert it to JUST a fill... you select it & the tool bar at left shows 2 squares at the bottom that represent fill & stroke, the lower right is for the stroke, & clicking on it to make it overlap in front of the fill square will allow you to reassign an attribute, like a different color, or in your case, the no-color choice which is represented by the red diagonal line either at the bottom of the tool bar OR in the colors dialog box.
..but if the object in question is just a stroke & you want to cut that, like an outline, then you need to convert the stroke to 2 different contours to be cut. That is done by selecting the object, & using the "object" pull-down menu, choose "path" & in the fly-out menu choose "outline stroke"
To expand on Doug's reply, you will find at times that various designers will use a stroke that is the same as the fill color to embolden some text or a graphic. Or it may be a contrasting color. If you wish to preserve the stroke as a vector, then you should:
Select the vector which has the stroke applied and click on Object > Path > Outline Path. In later versions of Illustrator, the menu command has changed to Outline Stroke ... but it does the same thing.