Fashion-MNIST is a dataset that is meant to be a direct replacement of the overused MNIST dataset. It is first introduced by Han Xiao and Kashif Rasul and Roland Vollgraf in their paper Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms.

Each data point in the Fashion-MNIST dataset is a 28x28 image flattened out as a vector of length 784 (just like MNIST). If you perform reshape to each vector and visualize the 28x28 image, you will see that the images are one of the following 10 items

T-shirt/top  
Trouser  
Pullover  
Dress  
Coat  
Sandal  
Shirt  
Sneaker  
Bag  
Ankle boot  

The above 10 items are labelled with integers from 0 to 9 respectively. 
The objective of the task is to come up with an algorithm to assign a label to a given image (a given 784 length vector) that matches with the true label.