Question: I have never heard this before, or maybe I have heard it in other terms?  

The context is that for adjacency lists, the time to list all vertices adjacent to *u* is `Θ(deg(u))`.  

 Similarly, the time to determine whether *(u,v)∈ E* is `O(deg(u))`.  

If the implementation of the adjacency list is an array, then I assume it would be constant time to find *u* in the array.  

 If all adjacent vertices are linked to *u*, then I believe it would take `O(n)` time to list or find all vertices, where n is the number of adjacent vertices.  

 Is that essentially what `Θ(deg(u))` means?

Answer: 
`Θ(deg(u))` = Big-Theta of the degree of `u` = the time is tightly-bounded (bounded from above and below) by the degree of vertices. In the case of an adjacency-list representation of the graph, the degree of a vertex `u` is `|adj[u]|` the size of the list for `u`.

Thus, to iterate over the adjacent vertices of `u` by an adjacency list is tightly-bound to the number of vertices adjacent to `u` (algorithmic facts sound redundant sometimes, don't they?).

The difference between Big-O and Big-Theta is that Big-O is an upper bound, whereas Big-Theta states a tight bound from above and below. That is, the same expression serves as a bound, but with a different coefficient m and x0. See [the family of Bachmann-Landau notations](http://en.wikipedia.org/wiki/Big_O_notation#Family_of_Bachmann.E2.80.93Landau_notations) on wikipedia.
I'm pretty sure `deg(u)` means "the degree of `u`", i.e. the number of edges that contain `u`. In an adjacency list representation, that number will also be the size of the adjacency list for `u`, so iterating it requires `Θ(|list|)`, which is `Θ(deg(u))`.