Having trouble understanding the x and y axis in SVM when training and testing data I wrote some code based on this article. 

In the code in the article they have created a partition of 80 percent test and 20 percent data

#What percentage of data you want to keep for training
percentage = 80
partition = int(len(hog_features)*percentage/100)


Later they have created the following variables, the data frame is two dimensions np array --- data_frame[hog_features,labels]:

x_train, x_test = data_frame[:partition,:-1],  data_frame[partition:,:-1]
y_train, y_test = data_frame[:partition,-1:].ravel() , data_frame[partition:,-1:].ravel()

clf.fit(x_train,y_train)


now what I don't understand is why for the second dimension of the array (the labels) for the x variables they're including everything except the last value and for the y variables the second dimension of the array is just including the last element of the array from what I can understand using array slicing (Maybe I'm wrong).
The answer to your questions is simply : that is how training works : 

The training set is a matrix in which the last column correspond to the labels and the rest correspond to the samples. 

When slicing  the matrix, you have two parts: the first one concerns the rows, the second one concerns the columns.

ROWS:

:partition means in fact the first 80% rows - this concerns the training set x_train, y_train

partition: means the last 20% rows - concerns the test set, x_test and y_test

COLUMNS:

:-1 mean all but the last column - concerns x_train and x_test

-1: mean just the last column - concerns y_train and y_test

Therefore, here you get for x_train and x_test everything but the last value. Be careful, in fact you get 80% of the data is for x_train (:partition) and 20% is for x_test (partition:). Now, for the labels you get only the last column, and 80% of the rows are for y_train while 20% of the rows are for y_test.

One more detail, your x_train and y_train is a 5D array, according to the documentation.