Answer:
It's irrelevant pseudoscientific nonsense, that's what it is. Same as if you were born on any other day.
If you're asking what "sign" you are... well, it depends on what system you use.
The most common is called the tropical system, under which someone born on July 23 would (probably) be a Leo, but might possibly be a Cancer instead (the 23rd is usually regarded as the first day of Leo, but in some years the Sun might still be "in Cancer" instead... more on why the quotation marks later).
In traditional sidereal astrology, July 23 is firmly Cancer, as Cancer runs from July 16 to August 15.
Neither of the two accurately reflects where the sun actually appears to be in the sky.
The traditional sidereal system is off because they divide the ecliptic (the path the Sun appears to trace through the sky over the course of a year) into 12 equal thirty degree signs, when in fact different constellations are different sizes, and the Sun is actually in the constellation of, say, Scorpio for only about a week, while it's in Leo or Pieces for roughly five times that long. Some astrologers attempt to justify this by pointing out that the IAU boundaries are somewhat arbitrary, and in some cases pass rather nearer to one of the asterisms the constellations are named for than the other.
The tropical system not only has the equal-30-degree sign problem, but additionally is based on ancient observations, which due to the precession of the equinoxes are now about 25 and a half days off.
In terms of "where the sun actually is", on July 23 it would be about two days into Cancer (July 21 - August 9, according to the boundaries as defined by the International Astronomical Union). A variation of the sidereal system uses the actual position of the sun relative to the constellation boundaries to determine the sign. In this system, July 23 would still be Cancer, the Sun having crossed the Gemini-Cancer boundary line on July 21. This system also includes a 13th (and in at least one variant a 14th) sign, Ophiuchus (joined in the 14 sign system by Cetus), and has the peculiar feature that in the month of May the sun briefly leaves Aries and enters Taurus, then after a couple of days leaves Taurus and passes into Aries again for two days, after which it re-enters Taurus until passing into Gemini about a month later.
(Note: the Sun passes near the boundary of Cetus, but never actually crosses it. It is, however, possible for the planets to occasionally appear in Cetus, since they do not orbit in precisely the same plane that Earth does.)