The term "meta-algorithm" has a fairly well-accepted meaning in the context of learning theory, which is the field of research from which multiplicative weights originates.
Specifically, a meta-algorithm, in the context of learning theory, is an algorithm that decides how to take a set of other (typically, though not necessarily non-meta) "algorithms" (which might be as dumb as a constant output, for example), and constructs a new algorithm out of those, often by combining or weighting the outputs of the component algorithms. (Don't take this to be a canonical definition though.) Typically those component algorithms are viewed as black-boxes taking input and producing their output, with the inner workings hidden/irrelevant.
There are a number of examples of meta-algorithms. The referenced Multiplicative Weighting algorithm is one example. A particularly simple example is majority voting for an ensemble of binary classifiers: Suppose you have a bunch of binary classification algorithms, and you don't know how to pick a good one. You can just compute them all, and let them vote. Voting in this case is the meta-algorithm. Of course, this may not work very well, and you might want to do something like weighted voting, where the weight somehow scales with observed performance.
Just a few examples of meta-algorithms that I can think of at the moment:
- multiplicative weights
- weighted majority
- ensemble averaging, voting
- "Follow the Leader"
As always, you can find examples that blur the line between meta and not meta. For example, K-nearest neighbors could be considered a weighted voting/averaging of component algorithms, where every potential neighbor (i.e. the labeled points in the dataset) is its own component algorithm, having a constant output, and the weighting is a function of distance from the algorithm input.