Humans or most of the organisms in this world can perceive three dimensions. Does buddhism explain about dimensions? If so how many are there?
The Sigalovada Sutta mention "the six directions":
At that time a young householder named Sigalaka arose early and set out from Rajagaha with freshly washed clothes and hair. With palms together held up in reverence, he was paying respect towards the six directions: that is east, south, west, north, lower and upper.
I take that to imply three dimensions.
It's not explicitly about dimensions but it casually implies in passing that there are three dimensions (perhaps as if it's the kind of thing that everyone knows and doesn't need explaining).
Modern maths (since the late 18th century) has described "time" as a kind of dimension. Buddhist texts imply that time, too, can be perceived.
Space (Akasa Pannattis) and time (Kala Pannattis) are a conceptual or perception based construct (Pannattis).
Many of the population can perceive in 3D: Stereopsis. There are some who cannot perceive in 3D: Stereoblindness. So the dimensionality differs from person to person or how you perceive it. Buddhism looks at the world through the experience of a being than a generalised truth independent of a observer and his experience of it.
See: Time and space: The Abhidhamma perspective, Professor K. N. Jayatilleke Memorial Lecture 2003 by Y. Karunadasa.. Also The Dhamma Theory by Y. Karunadasa which discusses Pannattis.