In igraph edge weights are represented via an edge attribute, called
‘weight’. The is_weighted function only checks that such an
attribute exists. (It does not even checks that it is a numeric edge
attribute.)
Edge weights are used for different purposes by the different functions.
E.g. shortest path functions use it as the cost of the path; community
finding methods use it as the strength of the relationship between two
vertices, etc. Check the manual pages of the functions working with weighted
graphs for details.