Where the decan sits
Signs divide into three faces of ten degrees each. This is the last of Aquarius, from twenty degrees to the end of the sign, after which the Sun enters Pisces.
The Sun passes through in about ten days, roughly 8 February to 18 February. As with every decan the edges are approximate. The tropical year overruns the calendar by close to a quarter of a day, so ingresses shift and then reset at each leap year, and a boundary can sit a day and a half from where a table places it. Mid February birthdays are the ones most affected here, since the end of this decan is also the end of the sign.
Venus one way, the Moon the other
Under the triplicity scheme the air signs are taken in order, Gemini, Libra, Aquarius, and each sign's decans start from itself. Aquarius is last, so its decans run Aquarius, Gemini, Libra, and the third falls to Libra, ruled by Venus.
The Chaldean order is a plain seven planet rotation, Mars, Sun, Venus, Mercury, Moon, Saturn, Jupiter, counted from zero degrees of Aries. The thirty third decan in that count is the Moon.
Venus and the Moon are not far apart in temperament, which makes this one of the less contradictory splits, but they are still different claims and they produce different emphases. It remains worth asking which scheme any given description was built on, since that is almost never stated.
What the tradition reads into it
Aquarius shaded by Libra is read as the sign at its most sociable. Aquarius on its own is described in terms of distance, principle and a preference for the general over the particular; the Libran overlay is taken to bring that back into contact with actual people, so the principles get argued face to face and the arrangements have to suit somebody. It is often called the most companionable stretch of the sign, meaning the least inclined to hold a position alone.
The Moon, from the Chaldean side, is read as adding responsiveness. The traditional associations are feeling, memory and the tidal quality of mood, and their appearance at the end of an air sign is taken to mean detachment that is not as complete as it looks. Older readings describe the combination as attentive to the room, which is not a quality Aquarius is usually credited with.
Take it as refinement rather than foundation. The decans reach us from Egyptian star lists that marked the hours of the night, and they are a genuine part of the tradition, but they sit above the sign reading and not underneath it.
The modes pull against each other slightly here too. Aquarius is fixed and Libra is cardinal, so the overlay is read as an opening in an otherwise settled sign, a willingness to start something with other people rather than simply hold a line. Combined with the Chaldean Moon it makes the closing degrees of Aquarius the part least like the sign's usual description, which is a common feature of third decans generally.
Other placements, and where the boundary really is
Nothing restricts this to the Sun. The Ascendant is read by decan very widely, because the rising degree is the most exactly determined point in a chart, and the Moon is read the same way. Any planet in the closing ten degrees of Aquarius carries this decan.
The check above computes your solar degree from your birth date and reports the decan and both rulers. Near 18 or 19 February the question is not only which decan but whether the Sun has already moved into Pisces, and that is a calculation rather than a lookup.
Questions people ask about this
What dates cover the third decan of Aquarius?
Roughly 8 to 18 February. The closing boundary is the Sun's entry into Pisces, which varies by up to a day and a half between years, so mid February birthdays should be calculated rather than looked up.
Who rules the third decan of Aquarius?
Venus under the triplicity scheme, by way of Libra. The Moon under the Chaldean order. Both are standard answers and they follow from different systems rather than from one being wrong.
What does Libra add to Aquarius?
The tradition reads it as bringing abstract principles into ordinary company, so positions get negotiated with people rather than held at a distance. It is described as the most sociable part of the sign.
Is the Moon an unusual ruler for an air decan?
It sits oddly with the sign's reputation for detachment, which is precisely why it is interesting. The Chaldean rotation does not consider the sign at all, so pairings like this occur throughout the sequence.
Do decans apply to placements other than the Sun?
Yes. Every point in a chart falls in a decan. The Ascendant and the Moon are both commonly read this way, and the Ascendant benefits most, since its degree is derived precisely from the birth time.
How much weight should a decan carry in a reading?
Less than the sign and much less than the chart as a whole. It is a refinement with a long history behind it, but a portrait built on the decan alone is a very narrow claim resting on very little.