Contrary to popular belief, we in the tropics do have seasons, even those of us who live close to the Equator. Earth's tilted axis affects us just as it affects those in the temperate latitudes. In our case in Colombia, for example, from May or so to maybe August, the sun is to the north of us, while the rest of the year it's to the south, just as in Chicago the winter sun is much lower on the southern horizon than is the summer sun.
Also contrary to what many believe, even here in Colombia, we are not in the southern hemisphere (except a little slice in our Amazon region). Most of the country is in the northern hemisphere, just above the Equator. So our summer (when we're most angled toward the sun) goes from May to September or so, just as in the US.
Nevertheless, we in Colombia confusingly call our hemispheric summer "winter", and our hemispheric winter "summer". This is thanks to those crazy Spaniards who colonized us. They came from a Mediterranean climate, where winters were cool and rainy, and summers hot and dry. These illiterate conquistadors likely didn't know much about hemispheres or meteorological phenomena, so when they got to Colombia they called our dry season "summer", and our rainy season "winter". But it so happens that in the tropics, the dry season occurs during our planetary winter, and the wet season occurs in summer, precisely the opposite of in the Mediterranean.
Here's a demonstration of how tropical seasons work. We'll call the part of the planet where the sun is directly overhead the "functional Equator". If our planet's axis were at a perfect right angle to the Sun, this functional Equator would correspond exactly to the midpoint between northern and southern hemispheres (the drawn, fixed line identified as the Equator on maps). Since our planet's axis is tilted 23 degrees, the fixed line we normally call the Equator (passing through Ecuador, the Congo, and Indonesia) only has the Sun directly overhead at two times of the year, the March and September Equinoxes. The rest of the year the Sun is either to the north (March to September) or to the south (September to March) of our fixed Equator line, so the functional Equator moves throughout the year.
This functional Equator, the point at which the sun falls directly overhead, is on average the hottest part of the planet. A column of hot air rises at this point, carrying with it lots of moisture from the Earth's surface.
Eventually this hot, moist air hits the stratosphere, which keeps it from going off into outer space. The air bounces off the stratosphere and is detoured to the north and the south. As the air has been rising from the functional Equator, it has been gradually cooling and losing water, which means that the functional Equator at any given time is where the most rain falls on the planet.
The northward- and southward-moving air keeps losing water along its path, so the rainfall diminishes as you move away from the functional Equator. Eventually the now-dry air is so cool that it falls to the Earth's surface again.
This point on the planet, where the dry air falls, is very dry. In fact, it comprises a dry belt running across the entire planet from East to West. Have you ever noticed that most of the Earth's deserts occur around 30 degrees latitude? Namibia, Australia, and the Atacama desert in the south, and the Sonora, Sahara, and Central Asia in the north.
This dry falling air in turn creates another convection cycle, creating other moist regions outside of the dry belts.
Because Earth's axis is tilted, the humid functional Equator and its accompanying dry belts move with respect to the planet's surface. Let's say we're at the northern limit of the tropics, like northern India. Our rainy season would go from around April to October, peaking in June, when the planet's alignment looks like the image above. While northern India is raining a lot in these months, Peru, at the southern limit of the tropics, is very dry. Just beyond these places, Italy's Mediterranean climate is dry in the summer months, while Chile's Mediterranean climate is wet at the same time. The cycle reverses itself during the northern hemisphere winter. This is the reason behind India's famous summer monsoons and very dry winters, and Italy's dry summers and wet winters.
We in Colombia, on the other hand, are located deeper within the tropics. So the rain hits us hard from maybe March to June, has a brief respite in July and August as the functional Equator passes to the north of us, and then the rain returns from September to November or so.
However, due to global climate change, our seasons are less reliable these days. The rainy season isn't always so rainy, and the dry season isn't always so dry. Or sometimes the rainy season is much wetter than normal, or the dry season much drier. Last year we had an exceptionally long and dry dry season, due in part to the seven-year El Nino phenomenon. This year we're in La Nina, which has poured rain down well into December, flooding much of the country. There are millions of weather refugees, mainly in the low, hot valleys surrounding our major rivers.
One quite surreal story that is typical of Colombia's daily magic realism involves the town of Gramalote. This small town in the Norte de Santander province recently disappeared. A combination of plate tectonics and heavy rains did it in. Much of our region of Colombia has weird geological problems. Roads constantly buckle at faultlines, and once our town's airport simply sunk into the ground. I guess this low-level tectonic activity is preferable to being in a hot earthquake zone (though quakes aren't unheard of here either). Anyway, Gramalote was apparently located on an opening faultline, which started moving and cracking all the buildings in the town. Then the heavy rains created landslides and exacerbated the opening faults. So in mid-December Gramalote was evacuated, and as far as I know has been swallowed by the Earth by now.
Here is a more detailed account in English of what happened in Gramalote.