The earth's rotational axis is tilted by about 23.5 degrees compared to the plane of its path around the sun. This would be analogous to leaning to one side as you walk. This means that, from the perspective of a viewer on earth, the height that the sun reaches in the sky will change throughout the year.
When the earth's axis is tilted toward the sun, and the viewer is in the northern hemisphere, the sun will appear high in the sky.
When the earth's axis is tilted away from the sun, and the viewer is in the northern hemisphere, the sun will appear lower in the sky.
These circumstances are reversed for the southern hemisphere, which is why the two hemispheres are said to have opposite seasons; when it's winter in the United States, Australia is on the half of the earth that is facing toward the sun, so it's summer there, and the sun is high in the sky.
The day when the sun reaches the highest (or lowest) point in the sky is called the solstice. The summer solstice for Los Angeles and Seattle is usually around June 21st. This would also be the day when the sun appears lowest in the southern hemisphere.
Things are more complex on the equator and the tropics in general. The sun never gets very low in the sky, and it actually has to pass through its "highest" point twice in the year. These two passes represent the transitional periods between the sun being high in the northern or southern hemisphere, aka spring and fall. These periods are called equinoxes. The equinoxes are around March 20th and September 22nd; these are the two days in which the sun would appear highest in Singapore.