There are different traditions of dividing the zodiac signs into parts, but one of the most enduring and suggestive is that of the 36 decans. According to this idea, each sign is split in three. The first part of the sign represents the "purest" type, whereas the second is somewhat influenced by the following sign in the same triplicity (element), and the third part again by the next sign of the element in counter-clockwise motion. This means that the first ten days of the sign of Aries is the purest Arian decan, the following ten days lends some qualities from Leo, the second fire sign in order, and finally the third decan has some affinity with Sagittarius.
While not in any way uncontroversial astrologically speaking, the idea is interesting and should be considered. Don't give it too much importance though. If you are born within the beginning ten days, you belong to first decan of your sign, the middle ten days the second, and so on. The notion can be applied to any planet placed in a zodiac sign, but is mostly used with sun signs.