GeoJSON Styling information

For GeoJSON - CSS styles are used to modify your points, line, polygons with thickness & color

{ 
    "type": "Feature",
    "geometry": {
    "type": "Polygon",
    "coordinates": [[
        [-180.0, 10.0], [20.0, 90.0], [180.0, -5.0], [-30.0, -90.0]
        ]]
    },
    "style": {
        "__comment": "all SVG styles allowed",
        "fill":"red",
        "stroke-width":"3",
        "fill-opacity":0.6
    },
    "className": {
        "baseVal":"A class name"
    }
}

http://wiki.openstreetmap.org/wiki/Geojson_CSS

These days there is Mapbox's SimpleStyle.

"properties": {
        // OPTIONAL: default ""
        // A title to show when this item is clicked or
        // hovered over
        "title": "A title",

        // OPTIONAL: default ""
        // A description to show when this item is clicked or
        // hovered over
        "description": "A description",

        // OPTIONAL: default "medium"
        // specify the size of the marker. sizes
        // can be different pixel sizes in different
        // implementations
        // Value must be one of
        // "small"
        // "medium"
        // "large"
        "marker-size": "medium",

        // OPTIONAL: default ""
        // a symbol to position in the center of this icon
        // if not provided or "", no symbol is overlaid
        // and only the marker is shown
        // Allowed values include
        // - Icon ID from the Maki project at http://mapbox.com/maki/
        // - An integer 0 through 9
        // - A lowercase character "a" through "z"
        "marker-symbol": "bus",

        // OPTIONAL: default "7e7e7e"
        // the marker's color
        //
        // value must follow COLOR RULES
        "marker-color": "#fff",

        // OPTIONAL: default "555555"
        // the color of a line as part of a polygon, polyline, or
        // multigeometry
        //
        // value must follow COLOR RULES
        "stroke": "#555555",

        // OPTIONAL: default 1.0
        // the opacity of the line component of a polygon, polyline, or
        // multigeometry
        //
        // value must be a floating point number greater than or equal to
        // zero and less or equal to than one
        "stroke-opacity": 1.0,

        // OPTIONAL: default 2
        // the width of the line component of a polygon, polyline, or
        // multigeometry
        //
        // value must be a floating point number greater than or equal to 0
        "stroke-width": 2,

        // OPTIONAL: default "555555"
        // the color of the interior of a polygon
        //
        // value must follow COLOR RULES
        "fill": "#555555",

        // OPTIONAL: default 0.6
        // the opacity of the interior of a polygon. implementations
        // may choose to set this to 0 for line features.
        //
        // value must be a floating point number greater than or equal to
        // zero and less or equal to than one
        "fill-opacity": 0.5
    }

GeoJSON doesn't deal with this. Any style information is going to depend on what the renderer is, Geojson CSS seams to target SVG but you also have Carto which targets mapnik, do remember that you can add extra fields to GeoJSON and it will still validate so none of these are invalid GeoJSON.