HOUSES are the 12 sectors of the sky which may vary in width, or more technically, may cover varying arcs, not the equal 30-degree arcs of the Signs. Depending upon how far from the equator an individual was born, some Houses may have smaller or larger arcs than others in a particular horoscope chart. (Only in the Equal House System is each House assumed to span exactly 30 degrees of arc.) The Houses are always numbered in a counter-clockwise order, with the First House cusp starting at the Ascendant. Houses which are exactly opposite each other are always the same width in degrees, even if they both happen to be wider or narrower than other Houses in the same horoscope chart.
If you lived in say, New York City, and were to watch the night sky from about five hours before sunrise until the Sun actually appeared above the horizon, you would notice that a given constellation might take more than the average of 2 hours to disappear below the western horizon, while the following constellation might take less than 2 hours to do the same; because northern latitudes like Toronto's are tilted away from the narrow band the constellations appear to move in (the zodiac), at any time of year except the day of the Summer or Winter Solstice (mid-summer and mid-winter, ie. the longest and shortest days, respectively).
Houses are defined in a way which corresponds to this natural phenomena, which in turn is a function of the rotation of the Earth we live on, and the 23.5-degree tilt of its poles relative to the plane of its orbit around the Sun (the plane called the Ecliptic). Think of a spinning top which is not quite vertical, and moving around on a turntable. If you drew an imaginary line through the center of the top, and parallel to the flat surface of the turntable, that would be similar to the plane of the ecliptic passing through the Earth at a 23.5 degree angle.
Houses are 12 in number, like the Signs, and are ordered in the same direction, but their starting point can be at any degree in any Sign, depending on the PLACE (latitude and longitude) and TIME of DAY (or night) and the DATE (month and year) you were born. It's a complicated calculation, best done by computers. The Cusp (initial boundary, or the starting line) of the First House is defined as the exact point (degree 1-30 of a Sign) which is just rising over the eastern horizon at the actual place you were born at the exact time you were born.
If you were born farther west, the Sun would rise later because it would take longer for the Earth to rotate towards the Sun so you could see it. For the same reason the point in any Sign which is just rising at the time of your own birth would be a slightly lower degree if you had been born a little farther west. That degree of the Sign would not have risen above the horizon yet, so your Ascendant would be a slightly lower degree of the Rising Sign, and your House Cusps would all be at slightly lower degrees too.
It may help to remember that as the Earth turns TOWARDS the Sun or any constellation of stars, then from our viewpoint ON Earth the Sun or any Sign with its background of stars will appear to RISE UP in the east and travel across the sky until it SETS below the horizon in the west. The LATER the time in minutes, the HIGHER will be the Sun or Moon or any Planet, AND the degree in any Sign that is rising. Signs appear to rise above the horizon in the same order they are traditionally listed, from Aries to Taurus to Pisces and back to Aries again. Since the horoscope chart has East on the LEFT and North at the TOP, the Signs and Houses have to appear in counter-clockwise order so that the chart shows them rising in their natural order.
To visualize the rising of the Signs, visualize the horoscope chart as a 12-spoked wagon wheel called "the Signs" with a second 12-spoked wheel called "the Houses" locked on top of it (but with their spokes not necessarily aligned) and turning clockwise once every 24 hours, so a new spoke turns past the horizontal line on the left about every two hours. But when you want to visualize the Sun (or the Moon and Planets) moving across the zodiac, think of a "sun-bug" crawling counter-clockwise along the rim of the Sign wheel even as the wheel itself is turning clockwise. The sun-bug will rise above the horizon line every 24 hours, even though it takes a whole year for the sun-bug to crawl once around the rim of the Sign wheel.
If you happened to be born exactly at sunrise, the Sun would also be in the Sign that was rising, and exactly on the horizon line at the point in the Sign which was also on the horizon; so your Rising Sign and your Ascendant Sign and degree and your Sun Sign and degree would all be exactly the same! An astrologer would call you a double Sign, such as "a double Leo", if both Sun/Ascendant or Moon/Ascendant (or Sun/Moon) are in the same Sign. If you were born in (approximately) the 2 hours JUST BEFORE sunrise, the Sun would be in your 1st House; and if it were within 5 degrees of the horizon, it would be said to be rising in the 1st House. If you were born in (approximately) the first 2 hours JUST AFTER sunrise, the Sun would be in your 12th House; and if it were within 5 degrees of the horizon it would be said to be rising in the 12th House. The term rising also applies to the Moon or any Planet positioned within 5 degrees of the Ascendant in any birth horoscope, whether it is below or above the horizon.
If you were born in the 2 hours just before NOON, when the Sun is highest overhead and approaching the Midheaven point, the Sun would be in your 10th House. Note that this applies on ANY DATE of the year, because the Ascendant and Midheaven and Houses are based on the Earth's rotation, which is what determines the TIME OF DAY. It is the Signs which are based on the time of YEAR, because the entire Earth revolves (orbits) around the Sun once a year. As it revolves, it also rotates, which is why astrologers must be aware of BOTH forms of motion and account for them in the birth horoscope chart.
Imagine yourself as a ballet dancer, spinning yourself around as you move around your partner who is standing still. From your eyes, you would see all the different sections of the scenery move past each time you spun around -- but at the same time, whenever you were facing your partner, you would observe him with a different part of the background behind him, depending on how far you had moved your whole body around him. That is pretty much like what is happening to the Earth, and we ride along with it like your eyes ride around in your body, seeing whatever lies in the direction you are facing at the time. Now if only you could imagine how things would look if you were able to maintain a 23.5 degree tilt towards the audience as you twirled around and circled your partner...