Eagerness is keen and impatient willingness. Wanting to start, and finding it hard to wait.
It takes to and a verb, so an eagerness to help or an eagerness to please, and that second phrase carries a faint warning, since being eager to please can shade into being unable to say no. The adjective eager is commoner than the noun. There is a fixed image in an eager beaver, meaning somebody enthusiastic to the point of irritating everybody else.
1nouneagernessKeen and impatient willingness to do something.
“His eagerness to help was slightly overwhelming.”
Middle English
egernesse
English, today
eagerness
From Middle English egernesse, egrenesse; equivalent to eager + ness.
Etymology from Wiktionary, CC BY-SA