Swollen lymph nodes (often called "glands") are very common in children, and usually don't mean anything serious is going on. Most commonly, these swell up to help the body fight infections, and go down in size as the infection is cleared.
Most infections are viral (for example, mono), though sometimes they're bacterial (like strep throat or a skin infection near the node, or cat scratch disease) If a child has significant fever or pain, it's a good idea to get evaluated. If the child just seems a bit run down and not quite himself, but not too sick, it's fine to wait a few days before going to the doctor.
Rarely, enlarged nodes are caused by other things. The OP mentioned Kawasaki Disease, which usually affects kids aged 1-5 years. KD includes prolonged fevers plus red eyes, rash, swollen hands/feel, swollen lips, and enlarged node(s) in the neck (not all of these findings are always present, but usually most of these findings are there within 5 days.)
Lymph nodes that are especially large or accompanied by significant illness should be evaluated right away, but ordinary nodes (say, the size of a marble) in a child who's not very sick can be safely observed for several days.