In a standard astrology chart, there are 10 planets (includes the Sun and Moon, excludes the Earth) and 12 houses. Each planet and house has different energy and rules different parts of our lives and personalities. Since there are less planets than houses, everyone has at least 2 (usually 3-5) houses with no planets in them. These are called empty houses.
Many people first hear about empty houses and worry that it means something bad. They'll never have love with an empty 7th house, or never have a career with an empty 10th house. But it doesn't actually mean that at all!
What's the deal with an empty house?
So, here's the situation - in astrology, when a house is considered empty, it means that you don't have as much to work on with that house. Whatever that house rules, there's less problems and lessons and all of that. It's believed you've already mastered that and don't have to deal with learning it again.
What is the 10th house?
The 10th house is the house of goals and direction, and corresponds to your Midheaven or Medium Coeli (the highest part of your chart). The 10th house is what you strive for in life, and is often associated with your career ambitions (but doesn't always have to be career, just whatever you're trying to achieve in life).
Normally, any planets in this house would be very important to your goals and professional life and direction. But, when you have no planets in the 10th house, it's entirely focused on the sign the 10th house falls in.
An Empty 10th House
Having an empty 10th house means you have less issues holding you back with achieving your goals, having direction, and knowing what you want in life. Much of how you do this and what you're focused on is seen with the sign the 10th house falls in, as well as what the ruler of that sign is doing in your chart. The ruler may have an oversized place in your goals and direction.
You may be someone who feels some sense of ease when you're working toward something, and you can create plans and follow them with less obstacles getting in the way. You can get the attention of important people and mentors, and you can be comfortable with recognition.
You can mature over time in a way that is natural and easy, and you can manage responsibilities with less uneasiness. You may become someone others admire, and you can be comfortable with this.
When it might be a challenge:
Chiron (ruler of wounds and healing) or the Lunar Nodes (the point's in the Moon's orbit where the Moon crosses the ecliptic; are spiritual/karmic in nature) in the 10th house can present challenges. They're not classified as planets, so they don't count with the empty house designation, but they can show there is much to work on. You may need to address old wounds and gain confidence with Chiron, and let go of baggage and embrace potential with the Lunar Nodes.
Chiron in the 10th house can show you pursuing work that involves healing or is spiritual in nature; the North Node in the 10th house can show you have great potential for success; and the South Node in the 10th house can show you may fall back to your goals and ambitions a little too much and need to develop more internally.
If the 10th house cusp is anaretic (at 29 degrees), or if the 10th house ruler is anaretic, this can show issues with using the energy fully and properly. You may run from goals and your direction, or be too obsessed with it, and need to find a proper focus.
The 10th house ruler intercepted (contained in a house), a singleton (only planet in an element, quality, or house type), or part of a challenging aspect configuration (like the apex planet of a t-square) can also show some challenges to work on.
Suggested Reading: The Empty Career Houses: Empty 2nd, 6th, and 10th Houses in Astrology