Aquarius connects to the future. It's always keeping an eye on how life will unfold far down the line, and therefore rules change.
The areas of life ruled by the house that falls in Aquarius can be areas where you experience lots of change in your life, and you can get restless when things aren't changing enough.
Aquarius is an air sign, along with Gemini and Libra. The air signs are the signs of the mind, and the social signs. They tend to be more flexible, and want to go with the way the wind blows.
Aquarius is also a fixed sign, along with Taurus, Leo, and Scorpio. The fixed signs are fixed in place, so this helps Aquarius to not just get blown around, but actually be able to tether itself at some point and focus.
Uranus, the planet of change, is the natural ruler of Aquarius. Uranus brings change, needs change, and learns from change, and opens up opportunities through change. Change is seen as a positive thing to Uranus.
1st house: The 1st house rules the self, so with an Aquarius 1st house, you may be someone who wants to change things constantly, in every way. You may take the reins with change, and you can also focus on changing your physical self often (new hair cut or hair color, new outfits, new styles, new shoes, etc.).
2nd house: The 2nd house rules money and values, so with an Aquarius 2nd house, you may be someone who experiences a lot of financial changes in your life, and money can come in big windfalls and go in big downturns (saving becomes important). Your values may also change throughout your life, and what you feel is worth your time and energy can change.
3rd house: The 3rd house rules communication and the mind, so with an Aquarius 3rd house, you may be someone who changes their mind a lot. You can experiment with ideas, and make changes to your plans on the fly. The ways you communicate may change, and you can change your perspectives often.
4th house: The 4th house rules the home and family, so with an Aquarius 4th house, you may be someone who experiences a lot of changes at home or with family. You may move a lot, constantly redecorate or renovate, and may get restless staying in one place for too long. Your family relationships and the people you think of as family may change throughout your life.
5th house: The 5th house rules love, so with an Aquarius 5th house, you may be someone who experiences a lot of changes in your love relationships. You may fall in and out of love quickly, and those you love may be prone to lots of change. What you love doing, your hobbies and creative ventures, may also change throughout your life.
6th house: The 6th house rules work and daily life, so with an Aquarius 6th house, you may be someone who experiences lots of small changes often. You can make changes to your routine and schedule regularly, and find that change can help you be more productive. The work you do may change throughout your life.
7th house: The 7th house rules relationships, so with an Aquarius 7th house, you may be someone who experiences lots of changes in your relationships. People may come and go in your life quickly, and you can connect with people fast, and commit quickly but walk away quickly too. You may attract people to your life who are constantly changing.
8th house: The 8th house rules transformations, so with an Aquarius 8th house, you may be someone who finds change to be transforming. You can use smaller changes to create bigger transformations, and you can feel strong when you make changes. Change can empower you, and you can take control.
9th house: The 9th house rules higher learning and travel, so with an Aquarius 9th house, you may be someone who changes what you're learning often, and you may be knowledgeable on a lot of random subjects. You can travel on a whim, and travel and learning may be ways for you to change.
10th house: The 10th house rules your goals and direction, so with an Aquarius 10th house, you may be someone who changes the direction you're going in small ways often, or in a big way once or twice in your life. You may need change regularly in your career and goals, otherwise you can get bored.
11th house: The 11th house rules your friends and dreams, so with an Aquarius 11th house, you may be someone who sees friends come and go in your life, and you may enter into friendships quickly and get out quickly. You may have lots of different dreams in your life, and your dreams can change throughout your life.
12th house: The 12th house rules the hidden, so with an Aquarius 12th house, you may be someone who experiences or creates changes quietly, on your own, without anyone paying attention. You can create massive changes this way, and it may not be so apparent on the outside. Your big changes tend to be internal, but can be quite intense.
Suggested Reading: Aquarius Houses: Where You're Different