The Lagrange multipliers in the context of SVMs are typically denoted $\alpha_i$. The fact that one often observes that most $\alpha_i=0$ is a direct consequence of the Karush-Kuhn-Tucker (KKT) dual complementarity conditions:
Since $y_i(\mathbf{w}^T\mathbf{x}_i+b) = 1$ iff $\mathbf{x}_i$ is on the SVM decision boundary, i.e. is a support vector assuming $\mathbf{x}_i$ is in the training set, and in most cases few training vectors are support vectors, as whuber pointed out in the comments, it means that most $\alpha_i$ are 0 or $C$.
Andrew Ng's CS229 Lecture notes on SVMs introduces the Karush-Kuhn-Tucker (KKT) dual complementarity conditions:
Note that we can create some case where all vectors in the training set are support vectors: e.g. see this Support Vector Machine Question.
