Meaning of variance in machine learning models
Variance actually measures the variability of the model prediction (say, for simplification, for a particular sample instance) if we would retrain the model multiple times (on different subsets of the data).

To gain an intuitive feeling of variance, suppose you have 100 training examples in your dataset (150 examples in total where 50 examples are reserved for a 50:50 split between validation and test sets). 

Pick a specific example from this set of 150 examples, say ${x}_{i}$. You are required to classify this in any one of the classes: ${k}_{1}, {k}_{2}, ..., {k}_{n}$.

Now randomly pick 100 samples from your original set of 150 samples (excluding your ${x}_{i}$). Now suppose you choose a hypothesis that has many higher degree terms, for instance: ${a}_{1}{x}^8 + {a}_{2}{x}^{7} + ... {a}_{0} = 0$ and do not regularise it, it will fit the model nicely and you get a low error on your training set.

You now run this model on ${x}_{i}$ and it predicts wrongly. You repeat the above process of having 100 samples five times and each time you get a different result, say ${k}_{a},    {k}_{b}, {k}_{c}, {k}_{d}$, and  ${k}_{e}$.

This variability in your prediction (coupled with the low error on your training set) implies your model is overfitting the data it is given. That's why it is not able to follow the general pattern in your data and is being affected by outliers more than it should.

I guess that answers your question about declaring a model as highly variant when 


  the predicted points are too prolonged