Deepnets are complex neural network models mostly adequate for big amounts of data. They can be used for both classification and regression problems, but their complexity goes against their interpretability. They have lots of coefficients and parameters, and BigML provides automated ways of looking for their best performing structure.
To learn about all their available configuration options using BigML's Dashboard, you can check the corresponding section of the Deepnets documentation. Also the Deepnets API documentation contains the information about the attributes that need to be specified to configure your source programmatically.