The Sidereal zodiac reflects where the planets were in the constellations of the sky at the time of your birth and where they always are.
The best way to understand this is to download a star tracking app so you can see in real time where the planets are. The more widely used tropical zodiac uses the equinoxes to determine the start of the zodiac. The spring equinox was just 2 days ago so according to tropical astrology the sun would now be in the sign of Aires. Sidereal astrologers and astronomers know that the sun remains in Pisces until the 13 of April, almost a month later.
The procession of the stars or equinox means that every 72 years the position of the Sun at the spring equinox moves back a single degree. Over the course of 2100 years the Sun will have moved back an entire sign and the whole process takes 26,000 years. This is confirmed by both modern science and ancient scholars. If you have heard about the dawning of the age of Aquarius you have heard of this concept.
A good rule of thumb for knowing your sidereal sun sign is that if you were born before the 14th of any month your sun sign isn't the one you think it is, but is in fact the previous sign. For example those born before the 14th of April are Pisces Suns rather than Aires. This will vary a little bit because of leap years and the continual movement of the constellations in relation to the Earths seasons but you can easily look this up in an ephemeris.
This can be rather hard to wrap your head around if you have been interested in astrology for some time and suddenly learn that you are a different sign, however it is a much more accurate system for making predictions and your Sun isn't even the most important sign of your chart--the ascendant and moon are of greater importance, and in that order.