If you have tons of something, you have an enormous amount of it, like when you buy tons of ice cream for your birthday party.
The informal tons is perfect for exaggerating, making a large quantity sound even bigger. You might say, "I have tons of friends at my new school" or "Your library is tiny — my library has tons more books!" It's a way to play up size or amount while still being vague. Tons comes from ton, which is often used colloquially ("I ate a ton of pasta"), but is also a precise unit for measuring weight.