What does the number of white bars in runway's threshold mean?
For runways built, refurbished or repainted after January 2008, the number of bars in the Threshold Markings indicates the width of the runway, as is described in Section 3 of the AIM. Older runways may still use an outdated scheme.

Runway threshold markings come in two configurations. They either consist of eight longitudinal stripes of uniform dimensions disposed symmetrically about the runway centerline, as shown in FIG 2-3-1, or the number of stripes is related to the runway width as indicated in TBL 2-3-2. A threshold marking helps identify the beginning of the runway that is available for landing. In some instances the landing threshold may be relocated or displaced.


(source: faa.gov)

Runway Width   | Number of Stripes 
==================================
60 feet (18 m) | 4
75 feet (23 m) | 6
100 feet (30 m)| 8
150 feet (45 m)| 12
200 feet (60 m)| 16 

With regard to how to tell the difference between Configuration A and B, Advisory AC 150/5340-1J goes into significantly more detail. It states that

The threshold markings may have either of the characteristics in (1) or (2) below, but after January 1, 2008, only those characteristics in (2) will be acceptable.

The details:

Configuration A. The runway threshold marking consists of eight longitudinal stripes of uniform dimensions spaced symmetrically about the runway centerline as shown in Figure 1. The stripes are 150 feet (45 m) long and 12 feet (3.6 m) wide and spaced 3 feet (1 m) apart, except for the center space, which is 16 feet (4.8 m). For runways less than 150 feet (45 m) in width, the length of the markings is not changed, but the width of the markings, spaces between markings and distance of markings from the runway edge are changed proportionally. For runways greater than 150 feet (45m) in width, the width of the markings and spaces between the markings may be increased proportionally or additional stripes may be added to both sides.
The rule for Configuration A markings requires scaling the width of the stripes and their spacings (and the outboard spacings from the runway edges) proportionally, keeping the length fixed. For a runway 150 feet wide the Configuration A stripes are 12 ft wide with 3 ft spacings (and an 8 ft spacing from the inboard stripe to the centreline, leaving 10 ft between the outboard and runway edge). The Configuration B stripes are given a fixed width of 5.75 ft with spacings of 5.75 ft also. If a Configuration A scheme were used on a narrow runway such that the stripes were equal to the width of the Configuration B stripes, the runway width would need to be about 72 feet (12 ft stripe width for a 150 ft runway width scaled to 5.75 ft for 71.875 ft). For a 72 ft wide runway bearing the Configuration A scheme the spacing between stripes would be reduced to slightly less than 1.5 ft. The difference between the schemes therefore ought to be apparent.

and

Configuration B. For this configuration, the number of stripes required is related to the runway width as indicated in Table 2. The stripes are 150 feet (45 m) long and 5.75 feet (1.75 m) wide and spaced 5.75 feet (1.75 m) apart except the center space is 11.5 feet (3.5 m) as shown in Figure 1. The outboard edges of the outboard stripes extend laterally to within 10 feet (3 m) of the edge of a runway or to a distance of 92 feet (27 m) on either side of a runway centerline, whichever results in the smaller lateral distance.

This is further borne out by a May 2004 advisory (CERTALERT 04-04) which states:

The purpose of this CERTALERT is to remind Airport Operators, Airport Certification Safety Inspectors, and Program Managers that paragraph 9(d) states the threshold markings may have either the characteristics in (1) Configuration A or (2) Configuration B, but after January 1, 2008, only those characteristics in (2) Configuration B will be acceptable.