Independent Samples:

When samples are collected from different populations which can have the same properties or the different ones. For example, a group of 1010 workers is selected from the "firm A" and a group of 1212 people are selected from the "firm B" to compare the income they earn per month.

Dependent Samples:

When the same sample is measured twice in two different conditions. For example, recording the scores of the students before giving them the training and recording the scores of those students again after providing training, to measure the effectiveness of the training.