Random state (Pseudo-random number) in Scikit learn
If there is no randomstate provided the system will use a randomstate that is generated internally. So, when you run the program multiple times you might see different train/test data points and the behavior will be unpredictable. In case, you have an issue with your model you will not be able to recreate it as you do not know the random number that was generated when you ran the program.
If you see the Tree Classifiers - either DT or RF, they try to build a try using an optimal plan. Though most of the times this plan might be the same there could be instances where the tree might be different and so the predictions. When you try to debug your model you may not be able to recreate the same instance for which a Tree was built. So, to avoid all this hassle we use a random_state while building a DecisionTreeClassifier or RandomForestClassifier.
PS: You can go a bit in depth on how the Tree is built in DecisionTree to understand this better.
randomstate is basically used for reproducing your problem the same every time it is run. If you do not use a randomstate in traintestsplit, every time you make the split you might get a different set of train and test data points and will not help you in debugging in case you get an issue.
From Doc:
If int, randomstate is the seed used by the random number generator; If RandomState instance, randomstate is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
I want to implement a machine learning algorithm in scikit learn, but I don't understand what this parameter random_state does? Why should I use it? 
I also could not understand what is a Pseudo-random number.