A computer program is any instruction sequence for the computer to automatically perform. It's a generic term including full executables, scripts, bytecode, whole applications or just sub routines etc.
Application software is a bit different in that it has a specific application. It solves a set of problems or fulfills a set of needs related to eachother. This includes games, word processors, music players and most of the software you use consciously and actively.
Utility software can be thought of narrow-focused meta applications. They generally aid and enhance the computer system itself by performing very specific tasks. Examples include most of the stuff you get in the /bin folder in your favorite freshly installed Linux distribution.
I could just have sent you the wikipedia links, but I trimmed it down for you 
Checking Wiki I found this description:
"Utility software is a kind of system software designed to help analyze, configure, optimize and maintain the computer. A single piece of utility software is usually called a utility or tool.
Utility software should be contrasted with application software, which allows users to do things like creating text documents, playing games, listening to music or surfing the web. Rather than providing these kinds of user-oriented or output-oriented functionality, utility software usually focuses on how the computer infrastructure (including the computer hardware, operating system, application software and data storage) operates. Due to this focus, utilities are often rather technical and targeted at people with an advanced level of computer knowledge.
Most utilities are highly specialized and designed to perform only a single task or a small range of tasks. However, there are also some utility suites that combine several features in one piece of software.
Most major operating systems come with several pre-installed utilities."
I guess that the word "program" fits for both examples above. Back in the day there was just programs and games. I too find these new namings a bit confusing since I'm not used to use them. Anyway I think it describes pretty well what an application is and what a utility is.
